diff options
| author | Karl Berry <karl@freefriends.org> | 2021-01-21 22:15:30 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2021-01-21 22:15:30 +0000 |
| commit | bbe24441779050c99ebbb179e03fc865124ce114 (patch) | |
| tree | a069c24e7232e520a55564d574115e7793f6ae62 | |
| parent | 2fa69371e59a0de5fceeede260cb87c85043ec54 (diff) | |
tkz-berge (21jan21)
git-svn-id: svn://tug.org/texlive/trunk@57485 c570f23f-e606-0410-a88d-b1316a301751
171 files changed, 8830 insertions, 1 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/NamedGraphs.pdf b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/NamedGraphs.pdf Binary files differnew file mode 100644 index 00000000000..9ca6ab3684a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/NamedGraphs.pdf diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Andrasfai.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Andrasfai.tex new file mode 100644 index 00000000000..41c7b2b578d --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Andrasfai.tex @@ -0,0 +1,63 @@ +%!TEX root = /Users/ego/Boulot/TKZ/tkz-berge/NamedGraphs/doc/NamedGraphs-main.tex +\newpage\section{Andrasfai graph} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Andrasfai +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grAndrasfai}{\oarg{options}\var{$k$}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/AndrasfaiGraph.html} + +\emph{The k-Andrásfai graph is a circulant graph on $3k-1$ nodes whose indices are given by the integers 1,\dots,$3k-1$ that are congruent to 1 (mod 3). +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +} + +\medskip +\end{NewMacroBox} + +\bigskip + +\subsection{\tkzname{Andrásfai graph : k=7, order 20}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{7} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Andrásfai graph : k=8, order 23}} + +\bigskip\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{8} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage +\subsection{\tkzname{Andrásfai graph : k=9, order 26}} + +\bigskip\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{9} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Balaban.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Balaban.tex new file mode 100644 index 00000000000..ee3870c80bf --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Balaban.tex @@ -0,0 +1,88 @@ +\newpage\section{Balaban}\label{balaban} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––– Balaban's graph ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grBalaban}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/Balaban10-Cage.html} + +\emph{The Balaban 10-cage is one of the three(3,10)-cage graphs (Read 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973; Pisanski 2001). Embeddings of all three possible (3,10)-cages (the others being the Harries graph and Harries-Wong graph) are given by Pisanski et al. (2001). Several embeddings are illustrated below, with the three rightmost being given by Pisanski and Randić (2000) +It is a Hamiltonian graph and has Hamiltonian cycles. It has 1003 distinct LCF notations, with four of length two (illustrated above) and 999 of length 1. +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +} +\end{NewMacroBox} + +\subsection{\tkzname{Balaban graph : first form}} +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grBalaban[form=1,RA=7,RB=3,RC=3] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage + +\subsection{\tkzname{Balaban graph : second form}} +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{blue!50} + \grBalaban[form=2,RA=7,RB=7,RC=4,RD=2.5] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Balaban graph : third form} } +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{brown}{orange} + \grBalaban[form=3,RA=7,RB=6.5,RC=5.6,RD=5.6,RE=4.6] + \end{tikzpicture} + \end{tkzexample} +\end{center} + + +\vfill\newpage + +\subsection{\tkzname{Balaban graph : Balaban 11-Cage}} + + +The Balaban 11-cage is the unique 11-cage graph, discovered by Balaban (1973) and proven unique by McKay and Myrvold (2003). It has 112 vertices, 168 edges, girth 11 (by definition), diameter 8 and chromatic number 3. + + +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture}[scale=.7] + \renewcommand*{\VertexInnerSep}{3pt} + \renewcommand*{\VertexLineWidth}{0.4pt} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{blue!50!black} + \grLCF[Math,RA=7]{% + 44,26,-47,-15,35,-39,11,-27,38,-37,43,14,28,51,-29,-16,41,-11,% + -26,15,22,-51,-35,36,52,-14,-33,-26,-46,52,26,16,43,33,-15,% + 17,-53,23,-42,-35,-28,30,-22, 45,-44,16,-38,-16,50,-55,20,28,% + -17,-43,47, 34,-26,-41,11,-36,-23,-16,41,17,-51,26,-33,47,17,% + -11,-20 ,-30,21,29,36,-43,-52,10,39,-28,-17,-52,51,26,37,-17,% + 10,-10,-45,-34,17,-26,27,-21,46,53,-10,29,-50,35,15,-47,-29,-41,% + 26,33,55,-17,42,-26,-36,16}{1} + \end{tikzpicture} +\end{tkzexample} + +\end{center} + + + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bipartite.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bipartite.tex new file mode 100644 index 00000000000..169ff1a4fcb --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bipartite.tex @@ -0,0 +1,134 @@ +\newpage\section{Complete BiPartite Graph}\label{bipart} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––– Complete BiPartite graph ––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grCompleteBipartite}{\oarg{options}\var{$p$}\var{$q$}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/CompleteBipartiteGraph.html} + +\emph{A complete bipartite graph is a bipartite graph (i.e., a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent) such that every pair of graph vertices in the two sets are adjacent. If there are $p$ and $q$ graph vertices in the two sets, the complete bipartite graph (sometimes also called a complete bigraph) is denoted $K_{p,q}$ . The below figures show $K_{3,2}$ and $K_{3,3}$. $K_{3,3}$ is also known as the utility graph (and the circulant graph $Ci_{1,3}(6)$), and is the unique 4-cage graph.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Complete_bipartite_graph} + +\emph{In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set. the graph $K_{1,3}$ is also called a claw.} +\end{NewMacroBox} + +\subsection{\tkzname{Complete bipartite graphs $K_{3,2}$ and $K_{3,3}$} } + %G=LCF_graph(6,[3,-3],3) +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=2,RB=2,RS=3]{3}{2} +\end{tikzpicture}\hspace*{2cm} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=2,RB=2,RS=3]{3}{3} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsection{\tkzname{Complete bipartite graphs $K_{3,5}$}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.5] + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=3,RB=2,RS=5]{3}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + +\subsection{\tkzname{Complete bipartite graph : $K_{18,18}$ }} + +The complete bipartite graph illustrated below plays an important role in the novel Foucault's Pendulum by Umberto Eco. + +\href{http://mathworld.wolfram.com/CycleGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\vfill +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90,scale=1.4] + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=0.5,RB=0.5,RS=9]{18}{18} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +A complete bipartite graph $K_{n,n}$ is a circulant graph (if the order is equal to $2n$ then $L=1,3,\dots,n$). +The code is on the next page + +\bigskip +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{6}{1,3} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{8}{1,3} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{10}{1,3,5} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{12}{1,3,5} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{14}{1,3,5,7} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{16}{1,3,5,7} +\end{tikzpicture} + +\vfill\newpage +\begin{tkzexample}[code only] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{6}{1,3} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{8}{1,3} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{10}{1,3,5} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{12}{1,3,5} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3]{14}{1,3,5,7} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3]{16}{1,3,5,7} +\end{tikzpicture} +\end{tkzexample} + + +\endinput + diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bull.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bull.tex new file mode 100644 index 00000000000..49fb3bb21b4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Bull.tex @@ -0,0 +1,24 @@ +\newpage\section{Bull} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Bull +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +The bull graph, 5 vertices, 5 edges, resembles to the head of a bull if drawn properly. +The bull graph is a simple graph on 5 nodes and 5 edges whose name derives from its resemblance to a schematic illustration of a bull + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[node distance=4cm] + \GraphInit[vstyle=Shade] + \Vertex{a0} + \NOEA(a0){a2} + \NOEA(a2){a4} + \NOWE(a0){a1} + \NOWE(a1){a3} + \Edges(a0,a1,a3) + \Edges(a0,a2,a4) + \Edge(a1)(a2) + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex new file mode 100644 index 00000000000..520b38555f4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex @@ -0,0 +1,43 @@ +\newpage\section{Cage}\label{cage} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Cage –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{Cage Graphs}{} + +\medskip +From Wikipedia \url{http://en.wikipedia.org/wiki/Cage_(graph_theory)}\\ +\emph{In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.\\ +Formally, an $(r,g)$-graph is defined to be a graph in which each vertex has exactly $r$ neighbors, and in which the shortest cycle has length exactly $g$. It is known that an $(r,g)$-graph exists for any combination of $r \geq 2$ and $g \geq 3$. An $(r,g)$-cage is an $(r,g)$-graph with the fewest possible number of vertices, among all $(r,g)$-graphs.} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/CageGraph.html}\\ +\emph{A $(r,g)$-cage graph is a $v$-regular graph of girth $g$ having the minimum possible number of nodes. When $v$ is not explicitly stated, the term "$g$-cage" generally refers to a $(3,g)$-cage.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +Examples : + +\medskip +\begin{tabular}{ll} + \bottomrule +$(r,g)$ & Names \\ +\midrule +$(3,3)$ & complete graph $K_4$ \\ +$(3,4)$ & complete bipartite graph $K_{3,3}$ Utility Graph\ref{bipart} \\ +$(3,5)$ & Petersen graph \ref{petersen} \\ +$(3,6)$ & Heawood graph \ref{heawood} \\ +$(3,7)$ & McGee graph \ref{mcgee} \\ +$(3,8)$ & Levi graph \ref{levi} \\ +$(3,10)$ & Balaban 10-cage \ref{balaban} \\ +$(3,11)$ & Balaban 11-cage \ref{balaban} \\ +$(3,12)$ & Tutte 12-cage \\ +$(4,3)$ & complete graph $K_5$ \\ +$(4,4)$ & complete bipartite graph $K_{4,4}$ \ref{bipart} \\ +$(4,5)$ & Robertson graph\ref{robertson} \\ +$(4,6)$ & Wong (1982)\ref{wong} \\ +\end{tabular} +\end{NewMacroBox} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Chvatal.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Chvatal.tex new file mode 100644 index 00000000000..72b5cd7e468 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Chvatal.tex @@ -0,0 +1,73 @@ +\newpage\section{Chvatal} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grChvatal}{\oarg{options}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Václav_Chvátal} + +\emph{Chvátal first learned of graph theory in 1964, on finding a book by Claude Berge in a Pilsen bookstore, and his first mathematical publication, at the age of 19, concerned directed graphs that cannot be mapped to themselves by any nontrivial graph homomorphism.\hfill\break +Gallery Theorem—which determines the number of guards required to survey the +walls of a polygonal art gallery (and has prompted much research), and constructed the smallest triangle-free 4-chromatic 4-regular graph, a beautiful graph now known as the Chvatal graph.} + + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/ChvatalGraph.html} + +\emph{The Chvátal graph is a quartic graph on 12 nodes and 24 edges. It has chromatic number 4, and girth 4.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Chvátal graph is implemented in \tkzname{tkz-berge} as \tkzcname{grChvatal} with three forms. +\end{NewMacroBox} + +\medskip +\subsection{\tkzname{Chvatal graph I}} + +\bigskip + +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \SetGraphShadeColor{blue!50!black}{blue}{gray} + \grChvatal[RA=6,RB=2] + \end{tikzpicture} + \end{tkzexample} + +\end{center} + +\vfill\newpage +\subsection{\tkzname{Chvatal graph II}} + +\bigskip +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue!50!black}{gray} + \grChvatal[form=2,RA=7,RB=4,RC=1.4] + \end{tikzpicture} + \end{tkzexample} + +\end{center} + + +\vfill\newpage +\subsection{\tkzname{Chvatal graph III}} + +\bigskip +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue!50!black}{gray} + \grChvatal[form=3,RA=7] + \end{tikzpicture} + \end{tkzexample} + +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cocktail_Party.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cocktail_Party.tex new file mode 100644 index 00000000000..3ed5e45ced4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cocktail_Party.tex @@ -0,0 +1,50 @@ +\newpage\section{Cocktail Party graph}\label{cocktail} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Cocktail Party –––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grCocktailParty}{\oarg{options}\var{integer}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/CocktailPartyGraph.html} + +\emph{The cocktail party graph of order , also called the hyperoctahedral graph (Biggs 1993, p. 17) is the graph consisting of two rows of paired nodes in which all nodes but the paired ones are connected with a graph edge. It is the graph complement of the ladder graph , and the dual graph of the hypercube graph.\hfill\break +This graph arises in the handshake problem. It is a complete n-partite graph that is denoted by Brouwer et al. (1989, pp. 222-223), and is distance-transitive, and hence also distance-regular.\hfill\break +The cocktail party graph of order is isomorphic to the circulant graph.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Chvátal graph is implemented in \tkzname{tkz-berge} as \tkzcname{grCocktailParty} with two forms. +\end{NewMacroBox} + +\subsection{\tkzname{Cocktail Party graph form 1 }} +\tikzstyle{VertexStyle} = [shape = circle, + shading = ball,% + ball color = green,% + minimum size = 24pt,% + draw] +\SetVertexMath +\tikzstyle{EdgeStyle} = [thick,% + double = orange,% + double distance = 1pt] +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \grCocktailParty[RA=3,RS=5]{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Cocktail Party graph form 2 }} + +\vspace*{2cm} +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \grCocktailParty[form=2,RA=4,RS=6]{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Coxeter.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Coxeter.tex new file mode 100644 index 00000000000..937ef0194ff --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Coxeter.tex @@ -0,0 +1,122 @@ +\newpage\section{Coxeter} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Coxeter ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +From MathWorld : \url{http://mathworld.wolfram.com/CoxeterGraph.html} + +The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges. + + +\subsection{\tkzname{Coxeter graph I}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90,scale=1] + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=5,prefix=a]{7} + \begin{scope}[rotate=-20]\grEmptyCycle[RA=4,prefix=b]{7}\end{scope} + \grCirculant[RA=3,prefix=c]{7}{2} + \grCirculant[RA=1.4,prefix=d]{7}{3} + \EdgeIdentity{a}{b}{7} + \EdgeIdentity{b}{c}{7} + \EdgeIdentity{b}{d}{7} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage +\subsection{\tkzname{Coxeter graph II}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=7,prefix=b]{24} + \grEmptyStar[RA=3,prefix=a]{4} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{0}{8}{2} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{7}{8}{2} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{18}{8}{2} + \EdgeDoubleMod{a}{4}{3}{0}{b}{24}{22}{8}{2} + \EdgeInGraphMod*{b}{24}{6}{5}{8} + \EdgeInGraphMod*{b}{24}{11}{1}{8} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage + +\subsection{\tkzname{Coxeter graph III}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=7,prefix=c]{7} + \grEmptyCycle[RA=6,prefix=b]{7} + \begin{scope}[rotate=12.85]\grEmptyCycle[RA=5,prefix=a]{14}\end{scope} + \EdgeIdentity{b}{c}{7} + \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{0}{2}{6} + \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{13}{2}{6} + \EdgeInGraphModLoop{a}{14}{4}{0}{0} + \EdgeInGraphModLoop{a}{14}{6}{1}{1} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Tutte-Coxeter graph ––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\vfill\newpage +\subsection{\tkzname{Tutte-Coxeter graph I}} + +\tikzstyle{VertexStyle} = [very thin,draw, + shape = circle, + color = white, + fill = black, + inner sep = 0pt, + minimum size = 18pt] +\tikzstyle{EdgeStyle} = [thick, + double = brown, + double distance = 1pt] + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=3] + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{cyan} + \begin{scope}[rotate=5]\grCycle[RA=2.5,prefix=a]{10}\end{scope} + \begin{scope}[rotate=-10]\grCirculant[RA=1.8,prefix=b]{10}{5}\end{scope} + \begin{scope}[rotate=36]\grCirculant[RA=1.1,prefix=c]{10}{3}\end{scope} + \EdgeIdentity{a}{b}{10} + \EdgeIdentity{b}{c}{10} + \end{tikzpicture} +\end{tkzexample} +\end{center} +% + +\vfill\newpage +\subsection{\tkzname{Tutte-Coxeter graph II}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{darkgray} + \grLCF[RA=7]{-13,-9,7,-7,9,13}{5} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Crown.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Crown.tex new file mode 100644 index 00000000000..c880642ca7c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Crown.tex @@ -0,0 +1,55 @@ +\newpage\section{Crown}\label{crown} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Crown ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grCrown}{\oarg{options}\var{integer}} + + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/CrownGraph.html} + +\emph{The Crown graph for an integer is the graph with vertex set +$\{x_0,x_1,\dots,x_{n-1},y_0,y_1,\dots,y_{n-1}\}$\hfill\break +and edge set \hfill\break +$\{(x_i,x_j): 0\leq i,j\leq n-1,i \not=j\}$.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Crown graph is implemented in \tkzname{tkz-berge} as \tkzcname{grCrown} with two forms. +\end{NewMacroBox} + + +\subsection{\tkzname{Crown graph form 1}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} +\tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = green, + minimum size = 24pt, + draw] +\tikzstyle{EdgeStyle} = [thick, + double = orange, + double distance = 1pt] +\SetVertexLabel\SetVertexMath +\grCrown[RA=3,RS=6]{4} + \end{tikzpicture} +\end{tkzexample} + +\end{center} + +\vfill\newpage +\subsection{\tkzname{Crown graph form 2}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCrown[form=2,RA=4,RS=6]{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-CubicSymmetric.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-CubicSymmetric.tex new file mode 100644 index 00000000000..32812490606 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-CubicSymmetric.tex @@ -0,0 +1,44 @@ +\newpage\section{Cubic Symmetric Graphs} +%<––––––––––––––––––––––––––––––––––––––––––––––––––--–––––––––––––––––––––––> +%<–––––––––––––––––––––––Cubic Symmetric Graphs –––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest and study. Since cubic graphs must have an even number of vertices, so must cubic symmetric graphs. + +The circulant graph , is illustrated below. + +\subsection{\tkzname{Cubic Symmetric Graph form 1}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \SetVertexNoLabel + \grLCF[RA=6]{3,-3}{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + +\subsection{\tkzname{Cubic Symmetric Graph form 2}} + +\vspace*{1cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] + \tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] + \grLCF[Math,RA=6]{3,-3}{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Desargues.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Desargues.tex new file mode 100644 index 00000000000..496041579be --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Desargues.tex @@ -0,0 +1,88 @@ +\newpage\section{Desargues}\label{desargues} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Desargues –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grDesargues}{\oarg{options}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Desargues_graph} + +\emph{ In the mathematical field of graph theory, the Desargues graph is a 3-regular graph with 20 vertices and 30 edges, formed as the Levi graph of the Desargues configuration.The Desargues graph can also be formed as a double cover of the Petersen graph, as the generalized Petersen graph G(10,3), or as the bipartite Kneser graph $H_{5,2}$.} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/DesarguesGraph.html} + +\emph{ The Desargues graph is a cubic symmetric graph distance-regular graph on 20 vertices and 30 edges, illustrated above in several embeddings. It can be represented in LCF notation as (Frucht 1976) and is isomorphic to the bipartite Kneser graph . It is the incidence graph of the Desargues configuration.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Desargues graph is implemented in \tkzname{tkz-berge} as \tkzcname{grDesargues} with two forms. +\end{NewMacroBox} + + +\tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] +\tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] +\SetVertexMath +\subsection{\tkzname{The Desargues graph : form 1}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \grDesargues[Math,RA=6] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The Desargues graph : form 2}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grDesargues[form=2,Math,RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{The Desargues graph wth \tkzname{LCF notation}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \grLCF[Math,RA=6]{5,-5,9,-9}{5} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage +\subsection{The Desargues graph with \tkzcname{grGeneralizedPetersen}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] + \tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] + \grGeneralizedPetersen[Math,RA=6]{10}{3} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Doyle.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Doyle.tex new file mode 100644 index 00000000000..4f6a55c1fc9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Doyle.tex @@ -0,0 +1,85 @@ +\newpage\section{Doyle}\label{doyle} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Doyle ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grDoyle}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/DoyleGraph.html} + +\emph{The Doyle graph, sometimes also known as the Holt graph (Marušič et al. 2005), is the symmetric quartic graph on 27 nodes illustrated. It is a Symmetric Graph. Three embeddings are illustrated below.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Doyle graph is implemented in \tkzname{tkz-berge} as \tkzcname{grDoyle} with three forms. +\end{NewMacroBox} + +\subsection{\tkzname{The Doyle graph : form 1}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{red}{Maroon}{fondpaille} + \SetVertexNoLabel + \grDoyle[RA=7,RB=5,RC=3] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The Doyle graph : form 2}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{red}{Magenta}{white} + \SetVertexNoLabel + \grDoyle[form=2,RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The Doyle graph : form 3}} +\begin{center} + \begin{tkzexample}[vbox] +\begin{tikzpicture} + \SetGraphArtColor{red}{Magenta}{red} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grDoyle[form=3,RA=7,RB=2] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage + +\subsection{27 nodes but not isomorphic to the Doyle graph} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \tikzstyle{VertexStyle} = [shape = circle, + ball color = gray!60, + minimum size = 16pt,draw] + \tikzstyle{EdgeStyle} = [thick,color=black,% + double = orange,% + double distance = 1pt] + \SetVertexNoLabel + \grCycle[RA=7.5]{9} + \grEmptyCycle[prefix=b,RA=5.5]{9} + \grCirculant[prefix=c,RA=3.5]{9}{4} + \EdgeIdentity{b}{c}{9} + \EdgeMod{a}{c}{9}{1} + \EdgeMod{a}{b}{9}{1} + \EdgeInGraphMod{b}{9}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Dyck.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Dyck.tex new file mode 100644 index 00000000000..dfa3a2aab51 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Dyck.tex @@ -0,0 +1,39 @@ +\newpage\section{Dyck graph}\label{dyck} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Nauru ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grDick}{\oarg{options}} + +From Wikipedia \url{http://en.wikipedia.org/wiki/Dyck_graph} + +\emph{In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It has chromatic number 2, radius 5, diameter 5 and girth 6. It is also a 3-vertex-connected and a 3-edge-connected graph. +} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/DyckGraph.html} + +\emph{The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated below in one of embeddings.} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + +\subsection{\tkzname{Dyck graph}} + +It can be represented in LCF notation as $\big[5,-5,13,-13\big]^8$ + + + +\subsection{\tkzname{Dyck graph with LCF notation}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grLCF[RA=7]{5,-5,13,-13}{8}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Folkman.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Folkman.tex new file mode 100644 index 00000000000..2c357f15cc1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Folkman.tex @@ -0,0 +1,118 @@ +\newpage\section{Folkman}\label{folkman} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Folkman –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grFolkman}{\oarg{options}} + +\medskip +From MathWorld : \url{http://mathworld.wolfram.com/FolkmanGraph.html} + +\emph{The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes 20.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + + +\subsection{\tkzname{Folkman Graph LCF embedding}} +The code is + +\begin{tkzexample}[code only] +\grLCF[RA=7]{5,-7,-7,5}{5}\end{tkzexample} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{darkgray} + \grFolkman[RA=6] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + + +\subsection{\tkzname{Folkman Graph embedding 1}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=45]% + \tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = gray!60, + inner sep = 3pt, + draw] + \tikzstyle{EdgeStyle} = [thick,orange] + \SetVertexNoLabel + \grCycle[prefix=a,RA=3]{4}% + \grCycle[prefix=b,RA=4]{4}% + \grCycle[prefix=c,RA=5]{4}% + \grCycle[prefix=d,RA=6]{4}% + \grCycle[prefix=e,RA=7]{4}% + \foreach \r/\s/\t in {a/d/e,b/e/a,c/a/b,d/b/c,e/c/d}{% + \Edges(\r0,\s1,\r2,\t3,\r0) + } + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + +\subsection{\tkzname{Folkman Graph embedding 1 new code}} +{ \tikzstyle{VertexStyle} =[shape = circle,% + shading = ball,% + inner sep = 4pt,% + draw] + \tikzstyle{EdgeStyle} = [thin,blue] + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} +\begin{scope}[shift={(1,1)},rotate=45]\grEmptyPath[prefix=a,RA=1]{5} + \end{scope} +\begin{scope}[shift={(-1,1)},rotate=135]\grEmptyPath[prefix=b,RA=1]{5} + \end{scope} +\begin{scope}[shift={(-1,-1)},rotate=225]\grEmptyPath[prefix=c,RA=1]{5} + \end{scope} +\begin{scope}[shift={(1,-1)},rotate=315]\grEmptyPath[prefix=d,RA=1]{5} + \end{scope} + \EdgeIdentity*{a}{b}{0,...,4} \EdgeIdentity*{b}{c}{0,...,4} + \EdgeIdentity*{c}{d}{0,...,4} \EdgeIdentity*{d}{a}{0,...,4} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{3}{1}{1} + \EdgeDoubleMod{a}{5}{2}{1}{b}{5}{0}{1}{2} + \EdgeDoubleMod{a}{5}{1}{1}{d}{5}{0}{1}{3} + \EdgeDoubleMod{c}{5}{2}{1}{b}{5}{0}{1}{2} + \EdgeDoubleMod{c}{5}{0}{1}{b}{5}{3}{1}{1} + \EdgeDoubleMod{c}{5}{1}{1}{d}{5}{0}{1}{3} + \Edges(a0,d4,c0) + \end{tikzpicture} +\end{tkzexample} +\end{center} +} +\vfill\newpage + +\subsection{\tkzname{Folkman Graph embedding 3}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.8] + \SetVertexNoLabel + \tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = gray!60, + inner sep = 3pt, + draw] + \tikzstyle{EdgeStyle} = [thick,orange] + \grEmptyCycle[prefix=a,RA=1.85]{5} \grEmptyCycle[prefix=b,RA=3.7]{5} + \grCycle[prefix=c,RA=6]{10} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{1}{1}{4} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{4}{1}{4} + \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{9}{2}{4} + \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{1}{2}{4} + \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{8}{2}{4} + \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{2}{2}{4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Foster.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Foster.tex new file mode 100644 index 00000000000..3f05835387d --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Foster.tex @@ -0,0 +1,39 @@ +\newpage\section{Foster}\label{foster} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Foster –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grFoster}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/FosterGraph.html} + +\emph{The Foster graph is a graph on 90 vertices and 135 arcs. It has a unique order-15 LCF notations.} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + \end{NewMacroBox} + +\subsection{\tkzname{Foster graph}} + +The macros is based on + +\begin{tkzexample}[code only] +\grLCF[Math,RA=7]{17, -9, 37, -37, 9, -17}{15}\end{tkzexample} + +\vspace*{1cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \renewcommand*{\VertexInnerSep}{2pt} + \renewcommand*{\EdgeLineWidth}{0.5pt} + \GraphInit[vstyle=Art] + \tikzset{VertexStyle/.append style={minimum size=2pt}} + \SetGraphColor{red}{blue} + \grLCF[Math,RA=6]{17, -9, 37, -37, 9, -17}{15} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex new file mode 100644 index 00000000000..b7f5bc4d661 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex @@ -0,0 +1,71 @@ +\newpage\section{Franklin}\label{franklin} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Franklin ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grFranklin}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/FranklinGraph.html} + +\emph{The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus providing the sole counterexample to the Heawood conjecture.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Franklin graph is implemented in \tkzname{tkz-berge} as \tkzcname{grFranklin}. +\end{NewMacroBox} + +\tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] +\tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] +\newcounter{tempi}\setcounter{tempi}{0} + +\subsection{\tkzname{The Franklin graph : embedding 1}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.7] + \grFranklin[Math,RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The Franklin graph : embedding 2}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCycle[Math,RA=4,prefix=a]{6} + \grCycle[Math,RA=6,prefix=b]{6} + \foreach \x in {0,...,5}{% + \ifthenelse{\isodd{\x}}{% + \pgfmathsetcounter{tempi}{\x-1}}{% + \pgfmathsetcounter{tempi}{\x+1}} + \Edge(a\x)(b\thetempi) +} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage +\subsection{\tkzname{The Franklin graph : with LCF notation embedding 3}} + +\space*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grLCF[Math,RA=7]{-5,-3,3,5}{3} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Gray.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Gray.tex new file mode 100644 index 00000000000..d2f16f91248 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Gray.tex @@ -0,0 +1,32 @@ +\newpage\section{Gray} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Gray –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +From MathWorld :\url{ http://mathworld.wolfram.com/GrayGraph.html} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + + +The Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnic et al. (2004) showed that the Gray graph is indeed the smallest possible cubic semisymmetric graph. + +It is the incidence graph of the Gray configuration. + +The Gray graph has a single order-9 LCF Notation and five distinct order-1 LCF notations. + +The Gray graph has girth 8, graph diameter 6 + +It can be represented in LCF notation as $\big[-25,7,-7,13,-13,25\big]^9$ + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{red} + \grLCF[Math,RA=6]{-25,7,-7,13,-13,25}{9} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Groetzsch.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Groetzsch.tex new file mode 100644 index 00000000000..491f9450d81 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Groetzsch.tex @@ -0,0 +1,88 @@ +\newpage\section{Groetzsch} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– groetzsch ––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grGrotzsch}{\oarg{options}\var{$k$}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Grötzsch_graph} + +\emph{The Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, and chromatic number 4. It is named after German mathematician Herbert Grötzsch, and its existence demonstrates that the assumption of planarity is necessary in Grötzsch's theorem (Grötzsch 1959) that every triangle-free planar graph is 3-colorable.} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/GroetzschGraph.html} + +\emph{The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski Graph of order four.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\end{NewMacroBox} + + +%GrotzschGraph +\tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = gray!60, + inner sep = 3pt, + draw] +\SetVertexNoLabel +\tikzstyle{EdgeStyle} = [thick,orange] + +\subsection{\tkzname{Grotzsch Graph : first form}} + +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture} + \grGrotzsch[RA=3,RB=6]{6}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage\null +\subsection{\tkzname{Grotzsch Graph : second form}} +\SetVertexLabel +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grGrotzsch[form=2,RA=6,RB=3]{6}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + + +\vfill\newpage\null +\subsection{\tkzname{Grotzsch Graph : third form}} +From Wikipedia : \url{http://en.wikipedia.org/wiki/Complete_bipartite_graph} + +\tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = blue!60, + inner sep = 6pt, + draw] +\SetVertexNoLabel +\tikzstyle{EdgeStyle} = [thick,double= red, + double distance = 1pt] + +\begin{center} + \begin{tkzexample}[vbox] + \begin{tikzpicture}[rotate=-18] + \draw[scale=.5,samples at={-6.4,-6.3,...,6.4}, + smooth,thick, + variable=\t, + double= red, + double distance = 1pt] + plot ({3*(1.5*cos(\t r) +3*cos(1.5*\t r))},% + {3*(1.5*sin(\t r) -3*sin(1.5*\t r))}); + \begin{scope}[rotate=36] + \grStar[prefix=a,RA=2.2]{6}% + \grEmptyCycle[prefix=b,RA=4.4]{5}% + \end{scope} + \end{tikzpicture} + \end{tkzexample} + +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Harries.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Harries.tex new file mode 100644 index 00000000000..88e5ca6df8f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Harries.tex @@ -0,0 +1,48 @@ +\newpage\section{Harries graph}\label{harries} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Nauru ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grHarries}{\oarg{options}} + +From Wikipedia \url{http://en.wikipedia.org/wiki/Harries_graph} + +\emph{In the mathematical field of graph theory, the Harries graph or Harries (3-10)-cage is a 3-regular undirected graph with 70 vertices and 105 edges. +The Harries graph has chromatic number 2, chromatic index 3, radius 6, diameter 6, girth 10 and is Hamiltonian. It is also a 3-vertex-connected and 3-edge-connected non-planar cubic graph.} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/HarriesGraph.html} + +\emph{The Harries graph has 678 distinct LCF notations, two of which are order 5 (illustrated below) and 674 of which are order 1..} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + +\subsection{\tkzname{Harries graph} with \tkzcname{grHarries}} + +The macro uses the LCF notation : $\big[-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29\big]^5$ + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grHarries[RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsection{\tkzname{Harries graph with LCF notation}} +It can be also represented in LCF notation as $\big[-35,9,15,-15,23,-27,27,-35,15,-15,-9,-27,27,-23\big]^5$ + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grLCF[RA=7]{-35,9,15,-15,23,-27,27,-35,15,-15,-9,-27,27,-23}{5}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex new file mode 100644 index 00000000000..1f8aec714a1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex @@ -0,0 +1,47 @@ +\newpage\section{Heawood graph}\label{heawood} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– HEAWOOD ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grHeawood}{\oarg{options}} + +\medskip +From Wikipedia \url{http://en.wikipedia.org/wiki/Heawood_graph} + +\emph{The Heawood graph is an undirected graph with 14 vertices and 21 edges. Each vertex is adjacent to exactly three edges (that is, it is a cubic graph), and all cycles in the graph have six or more edges. Percy John Heawood (1861-1955) was an English mathematician who spent a large amount of time on questions related to the four colour theorem.} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/HeawoodGraph.html} + +\emph{The Heawood graph is the unique $(3,6)$-cage graph and Moore graph and is graph illustrated below in one of his embeddings.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + +\subsection{\tkzname{Heawood graph}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.75] + \GraphInit[vstyle=Shade] + \grHeawood[RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +It can be represented in LCF notation as $\big[5,-5\big]^7$ + +\tkzcname{grLCF[RA=5]\{5,9\}\{7\}} gives the result because $-5 = 9\ mod\ 14$. + +\subsection{\tkzname{Heawood graph with LCF notation}}\label{lcf2} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grLCF[RA=7]{5,9}{7}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex new file mode 100644 index 00000000000..f13cca73bc7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex @@ -0,0 +1,41 @@ +\newpage\section{Hypercube} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Hypercube –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +From Wikipedia :\url{http://en.wikipedia.org/wiki/Hypercube_graph} + +In the mathematical field of graph theory, the hypercube graph $Q_n$ is a special regular graph with $2n$ vertices, which correspond to the subsets of a set with $n$ elements. Two vertices labelled by subsets S and T are joined by an edge if and only if S can be obtained from T by adding or removing a single element. Each vertex of $Q_n$ is incident to exactly $n$ edges (that is, $Q_n$ is $n$-regular), so the total number of edges is $2^{n-1}n$. +The name comes from the fact that the hypercube graph is the one-dimensional skeleton of the geometric hypercube. +Hypercube graphs should not be confused with cubic graphs, which are graphs that are 3-regular. The only hypercube that is a cubic graph is $Q_3$. + +\tikzstyle{VertexStyle} = [shape = circle,% + fill = red,% + inner sep = 3pt,% + outer sep = 0pt,% + draw] +\SetVertexNoLabel + +\subsection{\tkzname{The hypercube graph $Q_4$} } + +The code is on the next page. + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.75] + \grCycle[RA=8]{8} + \pgfmathparse{8*(1-4*sin(22.5)*sin(22.5))} + \let\tkzbradius\pgfmathresult + \grCirculant[prefix=b,RA=\tkzbradius]{8}{3} + \makeatletter + \foreach \vx in {0,...,7}{% + \pgfmathsetcounter{tkz@gr@n}{mod(\vx+1,8)} + \pgfmathsetcounter{tkz@gr@a}{mod(\vx+7,8)} + \pgfmathsetcounter{tkz@gr@b}{mod(\thetkz@gr@n+1,8)} + \Edge(a\thetkz@gr@n)(b\thetkz@gr@b) + \Edge(b\thetkz@gr@a)(a\vx) + } + \makeatother +\end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Koenisberg.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Koenisberg.tex new file mode 100644 index 00000000000..525d493fe1f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Koenisberg.tex @@ -0,0 +1,61 @@ +\newpage\section{The Seven Bridges of Königsberg}\label{seven} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––– Königsberg ––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grKonisberg}{\oarg{options}\var{$k$}} + +\medskip +From MathWorld : \url{http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html} + +\emph{The Königsberg bridge problem asks if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began. This is equivalent to asking if the multigraph on four nodes and seven edges (right figure) has an Eulerian circuit. This problem was answered in the negative by Euler (1736), and represented the beginning of graph theory.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg} + +\emph{The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory.\hfill\break +The Seven Bridges of Königsberg is a famous solved mathematics problem inspired by an actual place and situation. The city of Königsberg, Prussia (now Kaliningrad, Russia) is set on the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to walk a route that crosses each bridge exactly once.\hfill\break +In 1736, Leonhard Euler proved that it was not possible. In proving the result, Euler formulated the problem in terms of graph theory, by abstracting the case of Königsberg — first, by eliminating all features except the landmasses and the bridges connecting them; second, by replacing each landmass with a dot, called a vertex or node, and each bridge with a line, called an edge or link. The resulting mathematical structure is called a graph.} +\end{NewMacroBox} + +\subsection{\tkzname{Königsberg graph} with \tkzcname{grKonisberg}} +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture}[node distance=4cm] + \grKonisberg + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzcname{Königsberg graph} : fine embedding} +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture} + \renewcommand*{\VertexBallColor}{orange!50!red} + \renewcommand*{\EdgeDoubleDistance}{2pt} + \SetGraphUnit{4} + \GraphInit[vstyle=Shade] + \tikzset{LabelStyle/.style = {draw, + fill = yellow, + text = red}} + \Vertex{A} + \EA(A){B} + \EA(B){C} + {\SetGraphUnit{8} + \NO(B){D}} + \Edge[label=1](B)(D) + \tikzset{EdgeStyle/.append style = {bend left}} + \Edge[label=4](A)(B) + \Edge[label=5](B)(A) + \Edge[label=6](B)(C) + \Edge[label=7](C)(B) + \Edge[label=2](A)(D) + \Edge[label=3](D)(C) + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex new file mode 100644 index 00000000000..b0d5053f6fd --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex @@ -0,0 +1,79 @@ +\newpage\section{Levi Graph}\label{levi} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Levy –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grLevi}{\oarg{options}} + +\medskip + +From Wikipedia \url{http://en.wikipedia.org/wiki/Levi_graph} + +\emph{In combinatorics a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line.\hfil\break +In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth 8 it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle. } + +From MathWord : \url{http://mathworld.wolfram.com/LeviGraph.html} + +\emph{It has 30 nodes and 45 edges. It has girth 8, diameter 4, chromatic number 2. The Levi graph is a generalized polygon which is the point/line incidence graph of the generalized quadrangle . The graph was first discovered by Tutte (1947), and is also called the Tutte-Coxeter graph , Tutte's cage or "Tutte's (3,8)-cage".The Levi graph is the unique (3,8)-cage graph.\hfil\break +The incidence graph of a generic configuration is sometimes known as a Levi graph (Coxeter 1950).} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +Some examples of Levi Graphs with this definition are~: +\begin{itemize} +\item Desargues graph +\item Heawood graph +\item Heawood graph +\item Pappus graph +\item Gray graph +\item Tutte eight-cage +\end{itemize} + +\end{NewMacroBox} + +The two forms can be draw with : + + \begin{tkzexample}[code only] + \grLevi[RA=7]\end{tkzexample} + +and + + \begin{tkzexample}[code only] + \grLevi[form=2,RA=7,RB=5,RC=3]\end{tkzexample} + +You can see on the next pages, the two forms. +\vfill\newpage +Now I show you how to code this graph. + +\subsection{\tkzname{Levy graph :form 1}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \grLCF[prefix=a,RA=6]{-13,-9,7,-7,9,13}{5} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage + +\subsection{\tkzname{Levy graph :form 2}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCycle[prefix=a,RA=7]{10} + \EdgeInGraphMod{a}{10}{5} + \grEmptyCycle[prefix=b,RA=5]{10} + \grEmptyCycle[prefix=c,RA=3]{10} + \EdgeInGraphMod{c}{10}{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-McGee.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-McGee.tex new file mode 100644 index 00000000000..b72ec439db2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-McGee.tex @@ -0,0 +1,59 @@ +\newpage\section{Mc Gee}\label{mcgee} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Mc Gee –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grMcGee}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/McGeeGraph.html} + +\emph{The McGee graph is the unique 7-cage graph. It has 24 nodes, 36 edges, girth 7, diameter 4, and is a cubic graph. It has chromatic number 3.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\end{NewMacroBox} + +\bigskip +\subsection{\tkzname{McGee graph with }\tkzcname{grMcGee}} + +\bigskip +The same result is obtained with + +\begin{tkzexample}[code only] + \grLCF[Math,RA=6]{-12,7,-7}{8}\end{tkzexample} + +\medskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grMcGee[Math,RA=6] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +Others embeddings +\subsection{\tkzname{McGee graph with }\tkzcname{grLCF}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[Math,RA=6]{-12,-6,6,-12,7,-7,-12,6,-6,-12,7,-7}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{McGee graph with }\tkzcname{grLCF}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[Math,RA=6]{-12,6,-7,-12,7,-8,11,-6,6,-11,8,% + -7,-12,7,-6,-12,7,-11,-8,7,-7,8,11,-7}{1} + \end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex new file mode 100644 index 00000000000..111d5034539 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex @@ -0,0 +1,167 @@ +\newpage\section{Möbius-Kantor Graph}\label{moebius} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Moebius –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grMobiusKantor}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/Moebius-KantorGraph.html} + +\emph{The unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. It is 24 edges, girth 6, diameter 4, chromatic number 2, and is nonplanar but Hamiltonian. It can be represented in LCF notation and is identical to a generalized Petersen graph . +} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + + + + +\subsection{\tkzname{Möbius Graph : form I}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetGraphArtColor{red}{olive} + \SetVertexNoLabel + \grMobiusKantor[RA=7] +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Möbius Graph : form II}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=22.5] + \GraphInit[vstyle=Shade] + \SetGraphArtColor{red!50}{brown!50} + \SetVertexNoLabel + \grMobiusKantor[form=2,RA=7,RB=3] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + \subsection{\tkzname{Möbius Graph : form III}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grMobiusKantor[form=3,RA=7,RB=2] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Möbius Graph with LCF notation}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grLCF[RA=7]{5,-5}{8} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Möbius Graph with \tkzcname{grGeneralizedPetersen}} } + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grGeneralizedPetersen[RA=7,RB=4]{8}{3} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Moebius Ladder –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +A Möbius ladder of order $2n$ is a simple graph obtained by introducing a twist in a prism graph of order $2n$ that is isomorphic to the circulant graph with order $2n$ and $L=\{1,n\}$ + +\url{http://mathworld.wolfram.com/MoebiusLadder.html} + +\subsection{\tkzname{Möbius Ladder Graph}} + + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grMobiusLadder[RA=7,RB=2]{8}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage +\subsection{\tkzname{Circulant Graph isomorphic to the last graph}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grCirculant[RA=7]{16}{1,8}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput + +\newpage\section{Möbius-Kantor Graph}\label{MK} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––Möbius-Kantor Graph –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{% +\newmacro{Möbius-Kantor Graph : \tkzcname{grMobiusKantor}}}{lightgray} + \tkzcname{grMobiusKantor[|RA|=\meta{Number}]\var{Number}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/Moebius-KantorGraph.html} + +\emph{The unique cubic symmetric graph on 16 nodes, illustrated above in two embeddings. It is 24 edges, girth 6, diameter 4, chromatic number 2, and is nonplanar but Hamiltonian. It is identical to the generalized Petersen graph.} +\href{http://mathworld.wolfram.com/Moebius-KantorGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +The Möbius-Kantor Graph is implemented in \tkzname{tkz-berge} as \tkzcname{grMobiusKantor}. +\end{NewMacroBox} + +\subsection{Möbius-Kantor Graph with \tkzcname{grGeneralizedPetersen}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grGeneralizedPetersen[RA=7,RB=4]{3}{1} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage\null + + +\subsection{\tkzname{MobiusKantor graph}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grMobiusKantor[RA=5] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Nauru.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Nauru.tex new file mode 100644 index 00000000000..52d55f2d52c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Nauru.tex @@ -0,0 +1,37 @@ +\newpage\section{Nauru graph}\label{nauru} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Nauru ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grNauru}{\oarg{options}} + +From Wikipedia \url{http://en.wikipedia.org/wiki/Nauru_graph} + +\emph{TIn the mathematical field of graph theory, the Nauru graph is a symmetric bipartite cubic graph with 24 vertices and 36 edges. It was named by David Eppstein after the twelve-pointed star in the flag of Nauru. It has chromatic number 2, , diameter 4, radius 4 and girth 6. It is also a 3-vertex-connected and 3-edge-connected graph.} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/NauruGraph.html} + +\emph{The Nauru graph is the name given by Eppstein (2007) to the generalized Petersen graph GP(12,5) , which is also cubic symmetric graph , the permutation star graph of order 4, and the incidence graph of the Coxeter configuration. The name derives from the resemblance of the central star polygon in the generalized Petersen embedding to the 12-point star on the flag of the Pacific island nation of Nauru. The Nauru graph is graph illustrated below in one of his embeddings.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + +\subsection{\tkzname{Nauru graph}} + +It can be represented in LCF notation as $\big[5, −9, 7, −7, 9, −5\big]^4$ + +\tkzcname{grLCF[RA=5]\{5,9\}\{7\}} gives the result because $-5 = 9\ mod\ 14$. + +\subsection{\tkzname{Nauru graph with LCF notation}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grLCF[RA=7]{5, −9, 7, −7, 9, −5}{4}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Pappus.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Pappus.tex new file mode 100644 index 00000000000..539790b1d96 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Pappus.tex @@ -0,0 +1,61 @@ +\newpage\section{Pappus} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– Pappus ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grPappus}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/PappusGraph.html} + +\emph{A cubic symmetric distance-regular graph on 18 vertices, illustrated below in three embeddings. It can be represented in LCF notation $[5,7,-7,7,-7,-5]^3$ (Frucht 1976).} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +From Wikipedia : \url{http://en.wikipedia.org/wiki/Pappus_graph} +\emph{In the mathematical field of graph theory, the Pappus graph is a 3-regular graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is a distance-regular graph, one of only 14 such cubic graphs according to Cubic symmetric graphs.} + +This macro can be used with three different forms. +\end{NewMacroBox} + +\bigskip + + +\subsection{\tkzname{Pappus Graph : form 1}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \grPappus[RA=7] +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Pappus Graph : form 2}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPappus[form=2,RA=7,RB=5,RC=3] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Pappus Graph : form 3}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{blue} + \grPappus[form=3,RA=7,RB=5,RC=2.5] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Petersen.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Petersen.tex new file mode 100644 index 00000000000..1029e3252da --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Petersen.tex @@ -0,0 +1,175 @@ +%!TEX root = /Users/ego/Boulot/TKZ/tkz-berge/NamedGraphs/doc/NamedGraphs-main.tex +\newpage\section{Petersen}\label{petersen} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Petersen –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grPetersen}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/PetersenGraph.html} + +\emph{The Petersen graph is the graph , illustrated below in several embeddings, possessing 10 nodes, all of whose nodes have degree three. The Petersen graph is implemented in \tkzname{tkz-berge} as \tkzcname{grPetersen}. +The Petersen graph has girth 5, diameter 2, edge chromatic number 4, chromatic number 3.} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +From Wikipedia : \url{http://en.wikipedia.org/wiki/Petersen_graph} + +\emph{In graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in 1886.} + +This macro can be used with three different forms. +\end{NewMacroBox} + + \subsection{\tkzname{Petersen graph : form 1}} +\begin{center} +\begin{tkzexample}[latex=8cm] +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=1,RA=5,RB=3]% + \end{tikzpicture} +\end{tkzexample} +\end{center} +\vfill\newpage +\subsection{\tkzname{Petersen graph : form 2}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=2,RA=7,RB=3]% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Petersen graph : form 3}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=3,RA=7]% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The line graph of the Petersen graph}} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} +\GraphInit[vstyle=Art]\SetGraphArtColor{white}{blue} + \begin{scope}[rotate=-90] \grCirculant[RA=1.5,prefix=a]{5}{2}\end{scope} + \begin{scope}[rotate=-18] \grEmptyCycle[RA=4,prefix=b]{5}{2} \end{scope} + \begin{scope}[rotate=18] \grCycle[RA=7,prefix=c]{5} \end{scope} + \EdgeIdentity{a}{b}{5} + \EdgeIdentity{b}{c}{5} + \EdgeDoubleMod{b}{5}{0}{1}{a}{5}{2}{1}{5} + \EdgeDoubleMod{c}{5}{0}{1}{b}{5}{1}{1}{5} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Petersen Gen –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grGeneralizedPetersen}{\oarg{RA=\meta{Number},RB=\meta{Number}}\var{integer}\var{integer}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/GeneralizedPetersenGraph.html} + +\emph{The generalized Petersen graph , also denoted $GP(n,k)$ , for $n \geq 3$ and $1\leq k \leq \lfloor (n-1)/2\rfloor $ is a graph consisting of an inner star polygon (circulant graph ) and an outer regular polygon (cycle graph ) with corresponding vertices in the inner and outer polygons connected with edges. has nodes and edges. The Petersen graph is implemented in \tkzname{tkz-berge} as \tkzcname{grGeneralizedPetersen}.} +\href{http://mathworld.wolfram.com/GeneralizedPetersenGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Petersen_graph} +\emph{In 1950 H. S. M. Coxeter introduced a family of graphs generalizing the Petersen graph. These graphs are now called generalized Petersen graphs, a name given to them in 1969 by Mark Watkins. In Watkins' notation, $G(n,k)$ is a graph with vertex set\hfill\break + ${u_0, u_1,\dots, u_{n-1}, v_0, v_1, \dots, v_{n-1}}$\hfill\break +and edge set\hfill\break +${u_i u_{i+1}, u_i v_i, v_i u_{i+k}: i = 0,\dots,n-1}$\hfill\break +where subscripts are to be read modulo $n$ and $k<n/2$. Coxeter's notation for the same graph would be $\{n\}+\{n/k\}.$ +The Petersen Graph itself is $G(5,2)$ or $\{5\}+\{5/2\}$. +} + +This macro can be used with three different forms. +\end{NewMacroBox} + +\subsection{\tkzname{Generalized Petersen graph} GP(5,1)} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90,scale=.6] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{4pt} + \grGeneralizedPetersen[RA=5,RB=2]{5}{1} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{The Petersen graph} GP(5,2)} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{5}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Generalized Petersen graph} GP(6,2)} + +\vspace*{2cm}\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{6}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Generalized Petersen graph} GP(7,3)} + +\vspace*{2cm}\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{7}{3} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Generalized Petersen graph} GP(11,5)} + +\vspace*{2cm}\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90] + \renewcommand*{\VertexInnerSep}{8pt} + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \grGeneralizedPetersen[RA=7,RB=4]{11}{5} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex new file mode 100644 index 00000000000..a29fcf126be --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Platonic.tex @@ -0,0 +1,338 @@ +%!TEX root = /Users/ego/Boulot/TKZ/tkz-berge/NamedGraphs/doc/NamedGraphs-main.tex +\newpage\section{ The five Platonics Graphs} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Platonic graphs –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +The Platonic Graphs are the graphs formed by the edges and vertices of the five regular Platonic solids. The five Platonics Graphs are illustrated below. + +\begin{enumerate} + \item tetrahedral + \item octahedral + \item cube + \item icosahedral + \item dodecahedral +\end{enumerate} + + +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grTetrahedral}{\oarg{RA=Number}} +From MathWord : \url{http://mathworld.wolfram.com/TetrahedralGraph.html} + +\emph{\tkzname{Tetrahedral Graph} is the unique polyhedral graph on four nodes which is also the complete graph and therefore also the wheel graph . It is implemented as \tkzcname{grTetrahedral}} +\href{http://mathworld.wolfram.com/TetrahedralGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein} +} +It has : + +\begin{enumerate} + \item 4 nodes, + \item 6 edges, + \item graph diameter 1. +\end{enumerate} + +The Tetrahedral Graph is 3-Regular +\end{NewMacroBox} + +\subsection{\tkzname{Tetrahedral}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Shade] + \renewcommand*{\VertexInnerSep}{4pt} + \SetVertexNoLabel\SetGraphShadeColor{red!50}{black}{red} + \grTetrahedral[RA=5] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +\subsection{\tkzname{Tetrahedral LCF embedding}} + +\vspace*{2cm} +\begin{center} + \begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18] + \renewcommand*{\VertexInnerSep}{8pt} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{2,-2}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grOctahedral}{\oarg{RA=\meta{Number},RB=\meta{Number}}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/OctahedralGraph.html} + +\emph{\tkzname{Octahedral Graph} is isomorphic to the circulant graph $CI_{[1,2]}(6)$ . Two embeddings of this graph are illustrated below. It is implemented as \tkzcname{grOctahedral} or as \tkzcname{grSQCycle\{6\}}.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +It has : + +\begin{enumerate} + \item 6 nodes, + \item 12 edges, + \item graph diameter 2. +\end{enumerate} + +\medskip + The Octahedral Graph is 4-Regular. +\end{NewMacroBox} + + +\medskip +\subsection{\tkzname{Octahedral}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grOctahedral[RA=6,RB=2] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage\null +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grSQCycle[RA=5]{6} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage\null +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\medskip +\begin{NewMacroBox}{grCubicalGraph}{\oarg{RA=\meta{Number},RB=\meta{Number}}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/CubicalGraph.html} + +\emph{\tkzname{Cubical Graph} is isomorphic to a generalized Petersen graph $PG_{[4,1]}$, to a bipartite Kneser graph , to a crown graph and it is equivalent to the Cycle Ladder $CL(4)$. Two embeddings of this graph are illustrated below. It is implemented as \tkzcname{grCubicalGraph} or \tkzcname{grPrism\{4\}}.} +\href{http://mathworld.wolfram.com/CubicalGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +It has : + +\begin{enumerate} + \item 8 nodes, + \item 12 edges, + \item graph diameter 3. +\end{enumerate} + + The Cubical Graph is 3-Regular. +\end{NewMacroBox} + +\subsection{\tkzname{Cubical Graph : form 1}} +\begin{center} + \begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCubicalGraph[RA=5,RB=2] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage\null +\subsection{\tkzname{Cubical Graph : form 2}} +\begin{center} + \begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCubicalGraph[form=2,RA=7,RB=4] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Cubical LCF embedding}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{3,-3}{4} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grIcosahedral}{\oarg{RA=\meta{Number},RB=\meta{Number},RC=\meta{Number}}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/IcosahedralGraph.html} + +\emph{The \tkzname{Icosahedral Graph} is the Platonic graph whose nodes have the connectivity of the icosahedron, illustrated above in a number of embeddings. The icosahedral graph has 12 vertices and 30 edges. Since the icosahedral graph is regular and Hamiltonian, it has a generalized LCF notation.} +\href{http://mathworld.wolfram.com/IcosahedralGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +It has : + +\begin{enumerate} + \item 12 nodes, + \item 30 edges, + \item graph diameter 3. +\end{enumerate} + +\medskip + The Icosahedral Graph is 5-Regular. +\end{NewMacroBox} + +\medskip + +\subsection{\tkzname{Icosahedral forme 1 }} + +\tikzstyle{EdgeStyle}= [thick,% + double = orange,% + double distance = 1pt] + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{4pt} + \SetGraphArtColor{red}{orange} + \grIcosahedral[RA=5,RB=1] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage + +\subsection{\tkzname{Icosahedral forme 2 }} +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=-30] + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grIcosahedral[form=2,RA=8,RB=2,RC=.8] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage + +\subsection{\tkzname{Icosahedral} \tkzname{RA=1} et \tkzname{RB=7}} +\begin{center} +\begin{tkzexample}[vbox] + \begin{tikzpicture} + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grIcosahedral[RA=1,RB=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +\subsection{\tkzname{Icosahedral LCF embedding 1}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{-4,-3,4}{6} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +\subsection{\tkzname{Icosahedral LCF embedding 2}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{-2,2,3}{6} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\begin{NewMacroBox}{grDodecahedral}{\oarg{RA=\meta{Number},RB=\meta{Number},RC=\meta{Number},RD=\meta{Number}}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/DodecahedralGraph.html} + +\emph{The \tkzname{Icosahedral Graph} is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding shows a stereographic projection of the dodecahedron, the second an orthographic projection, the third is from Read and Wilson, and the fourth is derived from LCF notation.} +\href{http://mathworld.wolfram.com/DodecahedralGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +It has : + +\begin{enumerate} + \item 20 nodes, + \item 30 edges, + \item graph diameter 5. +\end{enumerate} + +\medskip + The Dodecahedral Graph is 3-Regular. +\end{NewMacroBox} + +\medskip +\subsection{\tkzname{Dodecahedral}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18,scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grDodecahedral[RA=7,RB=4,RC=2,RD=1] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsection{\tkzname{Dodecahedral other embedding}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCycle[RA=7,prefix=a]{10} + \grSQCycle[RA=4,prefix=b]{10} + \foreach \v in {0,...,9} + {\Edge(a\v)(b\v)} + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +\subsection{\tkzname{Dodecahedral LCF embedding}} + +\vspace*{2cm} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{10,7,4,-4,-7,10,-4,7,-7,4}{2} + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex new file mode 100644 index 00000000000..ce8807ce0b3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex @@ -0,0 +1,243 @@ +\newpage\section{Robertson}\label{robertson} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Robertson –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grRobertson}{\oarg{options}\var{$k$}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/RobertsonGraph.html} + +\medskip +\emph{The Robertson graph is the unique (4,5)-cage graph, illustrated below. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic graph.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\end{NewMacroBox} + +\subsection{\tkzname{Robertson graph with \tkzcname{grRobertson} }} + +The cage + +\medskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{black}{gray} + \grRobertson[RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\clearpage\newpage +\subsection{\tkzname{Fine embedding of the Robertson graph from RV}} + +\begin{center} + \begin{tikzpicture}[scale=.8] + \tikzstyle{TempEdgeStyle}= [thick,black,% + double = gray,% + double distance = 1.5pt]% + \SetVertexNoLabel + \renewcommand*{\VertexBigMinSize}{10pt} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \SetUpEdge[style = {thick,% + double = orange,% + double distance = 1pt}] + \SetGraphShadeColor{gray}{black}{gray} + \tikzstyle{EdgeStyle} = [TempEdgeStyle] + \begin{scope}[rotate=-30] + \grEmptyCycle[RA=5.4]{3} + \end{scope} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=10] + \grCycle[prefix=b,RA=4]{12} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \grCirculant[prefix=c,RA=2]{4}{2} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left] + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right] + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3} + \tikzstyle{EdgeStyle}=[TempEdgeStyle,in=-50,out=-120, + relative,looseness=2.5] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3} + \end{tikzpicture} +\end{center} + +\clearpage\newpage +Code for the Robertson Graph + +\medskip +\begin{tkzexample}[code only] +\begin{tikzpicture}[scale=.9] + \tikzstyle{TempEdgeStyle}= [thick,black,% + double = gray,% + double distance = 1.5pt]% + \SetVertexNoLabel + \renewcommand*{\VertexBigMinSize}{14pt} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \SetUpEdge[style = {thick,% + double = orange,% + double distance = 1pt}] + + \SetGraphShadeColor{gray}{black}{gray} + \tikzstyle{EdgeStyle} = [TempEdgeStyle] + \begin{scope}[rotate=-30] + \grEmptyCycle[RA=5.4]{3} + \end{scope} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=10] + \grCycle[prefix=b,RA=4]{12} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \grCirculant[prefix=c,RA=2]{4}{2} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left] + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right] + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3} + \tikzstyle{EdgeStyle}=[TempEdgeStyle,in=-50,out=-120, + relative,looseness=2.5] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3} + \end{tikzpicture} +\end{tkzexample} + +\clearpage\newpage +\subsection{\tkzname{Robertson graph with new styles}} + +The code with new styles, the result is on the next page. + +\bigskip +\begin{tkzexample}[code only] + \begin{tikzpicture}[scale=1] + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{red} + \begin{scope}[rotate=-30] + \grEmptyCycle[RA=5]{3} + \end{scope} + {\tikzset{EdgeStyle/.append style = {bend right=10}} + \grCycle[prefix=b,RA=3.5]{12}} + \grCirculant[prefix=c,RA=2]{4}{2} + {\tikzset{EdgeStyle/.append style = {bend left}} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4}} + {\tikzset{EdgeStyle/.append style = {bend right}} + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} + {\tikzset{EdgeStyle/.append style = {bend left=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3}} + {\tikzset{EdgeStyle/.append style = {bend right=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3}} + {\tikzset{EdgeStyle/.append style = {in=-50,out=-120,% + relative,looseness=2.5}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3}} + \end{tikzpicture} +\end{tkzexample} + +\begin{center} +\begin{tikzpicture}[scale=1] +\GraphInit[vstyle=Art] +\SetGraphArtColor{gray}{red} +\begin{scope}[rotate=-30] + \grEmptyCycle[RA=5]{3} +\end{scope} +{\tikzset{EdgeStyle/.append style = {bend right=10}} +\grCycle[prefix=b,RA=3.5]{12}} +\grCirculant[prefix=c,RA=2]{4}{2} +{\tikzset{EdgeStyle/.append style = {bend left}} +\EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4}} +{\tikzset{EdgeStyle/.append style = {bend right}} + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} +{\tikzset{EdgeStyle/.append style = {bend left=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3}} +{\tikzset{EdgeStyle/.append style = {bend right=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3}} + {\tikzset{EdgeStyle/.append style = {in=-50,out=-120,% + relative,looseness=2.5}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3}} +\end{tikzpicture} +\end{center} +\clearpage\newpage +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Robertson Wegner –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grRobertsonWegner}{\oarg{options}\var{$k$}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/Robertson-WegnerGraph.html} + +\medskip +\emph{he Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage . Like the other (5,5)-cages, the Robertson-Wegner graph has 30 nodes. It has 75 edges, girth 5, diameter 3, and chromatic number 4.} +\href{http://mathworld.wolfram.com/Robertson-WegnerGraph.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\end{NewMacroBox} + +\subsection{\tkzname{Robertson-Wegner graph}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90,scale=.6] + \GraphInit[vstyle=Art] + \tikzset{VertexStyle/.append style={minimum size=2pt}} + \grRobertsonWegner[RA=6] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +The next code gives the same result + +\begin{tkzexample}[code only] +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[RA=6]{6,12}{15} + \EdgeInGraphMod{a}{30}{9}{1}{6} \EdgeInGraphMod*{a}{30}{15}{2}{6} + \EdgeInGraphMod*{a}{30}{9}{3}{6} + \end{tikzpicture} +\end{tkzexample} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Tutte.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Tutte.tex new file mode 100644 index 00000000000..b97887549b6 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Tutte.tex @@ -0,0 +1,44 @@ +\newpage\section{Tutte-Coxeter}\label{tutte} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Tutte –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + + +\begin{NewMacroBox}{grTutteCoxeter}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/LeviGraph.html} + +\emph{The Levi graph is the unique (3,8)-cage graph and Moore graph. It is also distance-regular and is also called the Tutte-Coxeter graph or Tutte's 8-cage.} + +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\medskip +From Wikipedia : \url{http://en.wikipedia.org/wiki/Tutte–Coxeter_graph} + +\emph{In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth 8 it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle. The graph is named after William Thomas Tutte and H. S. M. Coxeter; it was discovered by Tutte (1947) but its connection to geometric configurations was investigated by both authors in a pair of jointly published papers (Tutte 1958; Coxeter 1958a).} +\end{NewMacroBox} + +\subsection{\tkzname{Tutte-Coxeter graph (3,8)-cage or Levi graph}} +An other method to get the same result is~: + +\medskip +\begin{tkzexample}[code only] + \grLCF[RA=7]{-13,-9,7,-7,9,13}{5}\end{tkzexample} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \tikzset{VertexStyle/.append style={minimum size=2pt}} + \SetGraphArtColor{blue}{darkgray} + \grTutteCoxeter +\end{tikzpicture} +\end{tkzexample} + +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Wong.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Wong.tex new file mode 100644 index 00000000000..70441c32f24 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Wong.tex @@ -0,0 +1,32 @@ +\newpage\section{Wong}\label{wong} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––-––––––––––––> +%<–––––––––––––––––––– Wong (5,5)-cages –––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––-–––––––> +\begin{NewMacroBox}{grWong}{\oarg{options}} + +\medskip +From MathWord : \url{http://mathworld.wolfram.com/WongGraph.html} + +\emph{The Wong graph is one of the four $(5,5)$-cage graphs. Like the other -cages, the Wong graph has 30 nodes. It has 75 edges, girth 5, diameter 3, chromatic number 4.} +\href{http://mathworld.wolfram.com/topics/GraphTheory.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + + +\subsection{\tkzname{Wong graph}} +You can see the cage definition here : \ref{cage} + +\bigskip +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=90,scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{blue} + \grWong[RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-couverture.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-couverture.tex new file mode 100644 index 00000000000..b39cf6e6250 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-couverture.tex @@ -0,0 +1,28 @@ +\thispagestyle{empty} +\null\vfill +\begin{center} +\textcolor{Brown}{\fontsize{30}{30}\selectfont{\upshape Gallery of named graphs}} + +\vspace{0.25cm} +\hfill\textcolor{Brown}{\fontsize{14}{14}\selectfont{\upshape with tkz-berge.sty by Alain Matthes}} +\end{center} + +\vspace{3cm} +\begin{tikzpicture}[scale=5] + \SetVertexNoLabel + \tikzstyle{VertexStyle} = [draw, + shape = circle, + shading = ball, + ball color = red!50, + inner sep = 10pt, + outer sep = 0pt] + \tikzstyle{EdgeStyle} = [thick,line width= 2pt,color=red] + \draw[fill = white,color = white] circle (0.55cm); + \draw (0,0) node[circle,draw,shade, + ball color = orange, + minimum size = 3cm] (am){\textbf{AlterMundus}}; + \grIcosahedral[RA=1.4,RB=0.8] +\end{tikzpicture} +\vfill\newpage\null\thispagestyle{empty} +\endinput + diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-main.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-main.tex new file mode 100644 index 00000000000..cfb4ba47ea4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-main.tex @@ -0,0 +1,192 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% NamedGraphs encodage : utf8 % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% Créé par Alain Matthes le 14/03/2007 % +% Copyright (c) 2021 __AlterMundus__ All rights reserved. % +% version : 1.1 % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License , either version 1.3 +% of this license or (at your option) any later version and/or +% 2. under the GNU Public License. +% See http://www.latex-project.org/lppl.txt for details. +% graphs from graph theory + +\documentclass[DIV = 14, + fontsize = 10, + headinclude = false, + footinclude = false, + index = totoc, + twoside, + headings = small]{tkz-doc} +\usepackage{etoc} +\gdef\tkznameofpack{NamedGraphs} +\gdef\tkzversionofpack{1.1} +\gdef\tkzdateofpack{2021/01/18} +\gdef\tkznameofdoc{NamedGraphs} +\gdef\tkzversionofdoc{1.1} +\gdef\tkzdateofdoc{2021/01/18} +\gdef\tkzauthorofpack{Alain Matthes} +\gdef\tkzadressofauthor{} +\gdef\tkznamecollection{AlterMundus} +\gdef\tkzurlauthor{} +\gdef\tkzengine{lualatex} +\gdef\tkzurlauthorcom{http://altermundus.fr} + + +% -- Packages --------------------------------------------------- +\usepackage[dvipsnames,svgnames]{xcolor} +\usepackage{calc} +\usepackage{tkz-berge} +\usetikzlibrary{calc,positioning,shapes} +\usepackage[colorlinks]{hyperref} +\hypersetup{ + linkcolor=Gray, + citecolor=Green, + filecolor=Mulberry, + urlcolor=NavyBlue, + menucolor=Gray, + runcolor=Mulberry, + linkbordercolor=Gray, + citebordercolor=Green, + filebordercolor=Mulberry, + urlbordercolor=NavyBlue, + menubordercolor=Gray, + runbordercolor=Mulberry, + pdfsubject={Euclidean Geometry}, + pdfauthor={\tkzauthorofpack}, + pdftitle={\tkznameofpack}, + pdfcreator={\tkzengine} +} + +\usepackage{tkzexample} + +%\usepackage[saved]{tkzexample} +%\def\tkzFileSavedPrefix{tkzNamed} +\usepackage{fontspec} +\setmainfont{texgyrepagella}% + [Extension = .otf , + UprightFont = *-regular, + ItalicFont = *-italic, + BoldFont = *-bold, + BoldItalicFont = *-bolditalic] +\setsansfont{texgyreheros}[ + Extension = .otf, + UprightFont = *-regular , + ItalicFont = *-italic , + BoldFont = *-bold , + BoldItalicFont = *-bolditalic , +] + +\setmonofont{lmmono10-regular.otf}[ + Numbers={Lining,SlashedZero}, + ItalicFont=lmmonoslant10-regular.otf, + BoldFont=lmmonolt10-bold.otf, + BoldItalicFont=lmmonolt10-boldoblique.otf, +] +\newfontfamily\ttcondensed{lmmonoltcond10-regular.otf} +%% (La)TeX font-related declarations: +\linespread{1.05} % Pagella needs more space between lines + +\usepackage{unicode-math} +\usepackage{fourier-otf,zorna} +\usepackage{datetime,multicol,lscape} +\usepackage[french]{babel} +\usepackage[autolanguage]{numprint} +\usepackage{microtype} +\usepackage{array,multirow,multido,booktabs} +\usepackage{shortvrb,fancyvrb} +\usepackage{fancybox} +\usepackage{stmaryrd} +\usepackage{xkeyval,array} +\usepackage[weather]{ifsym} +\RequirePackage{makeidx} +\makeindex + + +\title{The package : NamedGraphs} +\author{Alain Matthes} + +\AtBeginDocument{\MakeShortVerb{\|}} + + + + +%<---------------------------------------------------------------------------> +\begin{document} +\parindent=0pt +\author{\tkzauthorofpack} +\title{\tkznameofpack} +\date{\today} +\clearpage +\thispagestyle{empty} +\maketitle + +\clearpage + + +\nameoffile{\tkznameofpack} + +\defoffile{\tkzname{NamedGraphs.pdf} is not a beginner or advanced tutorial, not a study of graphs, it's only a gallery of undirected graphs made with the package \tkzname{tkz-berge.sty}. Some of graphs have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. \textbf{NamedGraphs.pdf} presents some of them. A lot of references can be found here \url{http://mathworld.wolfram.com} +} + +\presentation + +\vspace{1cm} + +\tkzHand Firstly, I would like to thank \textbf{Till Tantau} for the beautiful LATEX package, namely TikZ. + +\tkzHand I am grateful to \textbf{Michel Bovani} for providing the \tkzname{fourier} font. + +\tkzHand I received much valuable advice and guidance on Graph Theory from \textbf{Rafael Villarroel}\\ \url{http://graphtheoryinlatex.blogspot.com/}. + +\tkzHand The names of graphs can be found here \href{http://mathworld.wolfram.com/topics/SimpleGraphs.html}% + {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + + +\clearpage +\tableofcontents + +\clearpage\newpage + +\setlength{\parskip}{1ex plus 0.5ex minus 0.2ex} + +\input{NamedGraphs-Andrasfai.tex} +\input{NamedGraphs-Balaban.tex} +\input{NamedGraphs-Bipartite.tex} +\input{NamedGraphs-Bull.tex} +\input{NamedGraphs-Cage.tex} +\input{NamedGraphs-Cocktail_Party.tex} +\input{NamedGraphs-Coxeter.tex} +\input{NamedGraphs-Chvatal.tex} +\input{NamedGraphs-Crown.tex} +\input{NamedGraphs-Cubicsymmetric.tex} +\input{NamedGraphs-Desargues.tex} +\input{NamedGraphs-Doyle.tex} +\input{NamedGraphs-Folkman.tex} +\input{NamedGraphs-Foster.tex} +\input{NamedGraphs-Franklin.tex} +\input{NamedGraphs-Gray.tex} +\input{NamedGraphs-Groetzsch.tex} +\input{NamedGraphs-Heawood.tex} +\input{NamedGraphs-Hypercube.tex} +\input{NamedGraphs-Koenisberg.tex} +\input{NamedGraphs-Levi.tex} +\input{NamedGraphs-Mcgee.tex} +\input{NamedGraphs-Moebius.tex} +\input{NamedGraphs-Pappus.tex} +\input{NamedGraphs-Petersen.tex} +\input{NamedGraphs-Platonic.tex} +\input{NamedGraphs-Robertson.tex} +\input{NamedGraphs-Tutte.tex} +\input{NamedGraphs-Wong.tex} + +\clearpage\newpage +\printindex +\end{document} + diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-1-0.tex new file mode 100644 index 00000000000..41f9be6502a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{7} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-2-0.tex new file mode 100644 index 00000000000..b9382cd1855 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-2-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{8} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-3-0.tex new file mode 100644 index 00000000000..36ce893fe1c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-1-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grAndrasfai[RA=7]{9} +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-1-0.tex new file mode 100644 index 00000000000..3d0e57f776a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-1-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \SetVertexNoLabel + \grLCF[RA=6]{3,-3}{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-2-0.tex new file mode 100644 index 00000000000..1078db0a100 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-10-2-0.tex @@ -0,0 +1,24 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] + \tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] + \grLCF[Math,RA=6]{3,-3}{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-1-0.tex new file mode 100644 index 00000000000..57bf0742879 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-1-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \grDesargues[Math,RA=6] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-2-0.tex new file mode 100644 index 00000000000..7802a9c2ae4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-2-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grDesargues[form=2,Math,RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-3-0.tex new file mode 100644 index 00000000000..7d43cca61b9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-3-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \grLCF[Math,RA=6]{5,-5,9,-9}{5} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-4-0.tex new file mode 100644 index 00000000000..3b894009c25 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-11-4-0.tex @@ -0,0 +1,24 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \tikzstyle{VertexStyle} = [shape = circle,% + color = white, + fill = black, + very thin, + inner sep = 0pt,% + minimum size = 18pt, + draw] + \tikzstyle{EdgeStyle} = [thick,% + double = brown,% + double distance = 1pt] + \grGeneralizedPetersen[Math,RA=6]{10}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-1-0.tex new file mode 100644 index 00000000000..aaad85f436f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-1-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{red}{Maroon}{fondpaille} + \SetVertexNoLabel + \grDoyle[RA=7,RB=5,RC=3] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-2-0.tex new file mode 100644 index 00000000000..f70511ef9ce --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-2-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{red}{Magenta}{white} + \SetVertexNoLabel + \grDoyle[form=2,RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-3-0.tex new file mode 100644 index 00000000000..40c9d752a71 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-3-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \SetGraphArtColor{red}{Magenta}{red} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grDoyle[form=3,RA=7,RB=2] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-4-0.tex new file mode 100644 index 00000000000..3199fdf61a6 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-12-4-0.tex @@ -0,0 +1,27 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \tikzstyle{VertexStyle} = [shape = circle, + ball color = gray!60, + minimum size = 16pt,draw] + \tikzstyle{EdgeStyle} = [thick,color=black,% + double = orange,% + double distance = 1pt] + \SetVertexNoLabel + \grCycle[RA=7.5]{9} + \grEmptyCycle[prefix=b,RA=5.5]{9} + \grCirculant[prefix=c,RA=3.5]{9}{4} + \EdgeIdentity{b}{c}{9} + \EdgeMod{a}{c}{9}{1} + \EdgeMod{a}{b}{9}{1} + \EdgeInGraphMod{b}{9}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-1-0.tex new file mode 100644 index 00000000000..80fb6827231 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{darkgray} + \grFolkman[RA=6] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-2-0.tex new file mode 100644 index 00000000000..c4ced93e3a2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-2-0.tex @@ -0,0 +1,28 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=45]% + \tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = gray!60, + inner sep = 3pt, + draw] + \tikzstyle{EdgeStyle} = [thick,orange] + \SetVertexNoLabel + \grCycle[prefix=a,RA=3]{4}% + \grCycle[prefix=b,RA=4]{4}% + \grCycle[prefix=c,RA=5]{4}% + \grCycle[prefix=d,RA=6]{4}% + \grCycle[prefix=e,RA=7]{4}% + \foreach \r/\s/\t in {a/d/e,b/e/a,c/a/b,d/b/c,e/c/d}{% + \Edges(\r0,\s1,\r2,\t3,\r0) + } + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-3-0.tex new file mode 100644 index 00000000000..08f313a2052 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-3-0.tex @@ -0,0 +1,30 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} +\begin{scope}[shift={(1,1)},rotate=45]\grEmptyPath[prefix=a,RA=1]{5} + \end{scope} +\begin{scope}[shift={(-1,1)},rotate=135]\grEmptyPath[prefix=b,RA=1]{5} + \end{scope} +\begin{scope}[shift={(-1,-1)},rotate=225]\grEmptyPath[prefix=c,RA=1]{5} + \end{scope} +\begin{scope}[shift={(1,-1)},rotate=315]\grEmptyPath[prefix=d,RA=1]{5} + \end{scope} + \EdgeIdentity*{a}{b}{0,...,4} \EdgeIdentity*{b}{c}{0,...,4} + \EdgeIdentity*{c}{d}{0,...,4} \EdgeIdentity*{d}{a}{0,...,4} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{3}{1}{1} + \EdgeDoubleMod{a}{5}{2}{1}{b}{5}{0}{1}{2} + \EdgeDoubleMod{a}{5}{1}{1}{d}{5}{0}{1}{3} + \EdgeDoubleMod{c}{5}{2}{1}{b}{5}{0}{1}{2} + \EdgeDoubleMod{c}{5}{0}{1}{b}{5}{3}{1}{1} + \EdgeDoubleMod{c}{5}{1}{1}{d}{5}{0}{1}{3} + \Edges(a0,d4,c0) + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-4-0.tex new file mode 100644 index 00000000000..75f7017f00d --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-13-4-0.tex @@ -0,0 +1,28 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.8] + \SetVertexNoLabel + \tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = gray!60, + inner sep = 3pt, + draw] + \tikzstyle{EdgeStyle} = [thick,orange] + \grEmptyCycle[prefix=a,RA=1.85]{5} \grEmptyCycle[prefix=b,RA=3.7]{5} + \grCycle[prefix=c,RA=6]{10} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{1}{1}{4} + \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{4}{1}{4} + \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{9}{2}{4} + \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{1}{2}{4} + \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{8}{2}{4} + \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{2}{2}{4} +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-14-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-14-1-0.tex new file mode 100644 index 00000000000..1ee8a1a8c1f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-14-1-0.tex @@ -0,0 +1,19 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \renewcommand*{\VertexInnerSep}{2pt} + \renewcommand*{\EdgeLineWidth}{0.5pt} + \GraphInit[vstyle=Art] + \tikzset{VertexStyle/.append style={minimum size=2pt}} + \SetGraphColor{red}{blue} + \grLCF[Math,RA=6]{17, -9, 37, -37, 9, -17}{15} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-1-0.tex new file mode 100644 index 00000000000..601154c67c1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-1-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.7] + \grFranklin[Math,RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-2-0.tex new file mode 100644 index 00000000000..f6779611911 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-2-0.tex @@ -0,0 +1,21 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCycle[Math,RA=4,prefix=a]{6} + \grCycle[Math,RA=6,prefix=b]{6} + \foreach \x in {0,...,5}{% + \ifthenelse{\isodd{\x}}{% + \pgfmathsetcounter{tempi}{\x-1}}{% + \pgfmathsetcounter{tempi}{\x+1}} + \Edge(a\x)(b\thetempi) +} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-3-0.tex new file mode 100644 index 00000000000..9ea14cf74ce --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-15-3-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grLCF[Math,RA=7]{-5,-3,3,5}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-16-0-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-16-0-0.tex new file mode 100644 index 00000000000..05c9d2ec509 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-16-0-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{red} + \grLCF[Math,RA=6]{-25,7,-7,13,-13,25}{9} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-1-0.tex new file mode 100644 index 00000000000..9b75eea0771 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-1-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \grGrotzsch[RA=3,RB=6]{6}% + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-2-0.tex new file mode 100644 index 00000000000..994cef0a799 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-2-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grGrotzsch[form=2,RA=6,RB=3]{6}% + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-3-0.tex new file mode 100644 index 00000000000..9994c13ae6c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-17-3-0.tex @@ -0,0 +1,24 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[rotate=-18] + \draw[scale=.5,samples at={-6.4,-6.3,...,6.4}, + smooth,thick, + variable=\t, + double= red, + double distance = 1pt] + plot ({3*(1.5*cos(\t r) +3*cos(1.5*\t r))},% + {3*(1.5*sin(\t r) -3*sin(1.5*\t r))}); + \begin{scope}[rotate=36] + \grStar[prefix=a,RA=2.2]{6}% + \grEmptyCycle[prefix=b,RA=4.4]{5}% + \end{scope} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-1-0.tex new file mode 100644 index 00000000000..66782736c6a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-1-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}% + \GraphInit[vstyle=Shade] + \grHeawood[RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-2-0.tex new file mode 100644 index 00000000000..05e2c80afb4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-18-2-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grLCF[RA=7]{5,9}{7}% + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-19-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-19-1-0.tex new file mode 100644 index 00000000000..a320c8bc940 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-19-1-0.tex @@ -0,0 +1,26 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCycle[RA=8]{8} + \pgfmathparse{8*(1-4*sin(22.5)*sin(22.5))} + \let\tkzbradius\pgfmathresult + \grCirculant[prefix=b,RA=\tkzbradius]{8}{3} + \makeatletter + \foreach \vx in {0,...,7}{% + \pgfmathsetcounter{tkz@gr@n}{mod(\vx+1,8)} + \pgfmathsetcounter{tkz@gr@a}{mod(\vx+7,8)} + \pgfmathsetcounter{tkz@gr@b}{mod(\thetkz@gr@n+1,8)} + \Edge(a\thetkz@gr@n)(b\thetkz@gr@b) + \Edge(b\thetkz@gr@a)(a\vx) + } + \makeatother +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-1-0.tex new file mode 100644 index 00000000000..092d89b07fd --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grBalaban[form=1,RA=7,RB=3,RC=3] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-2-0.tex new file mode 100644 index 00000000000..6d8375a0b8f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-2-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{blue!50} + \grBalaban[form=2,RA=7,RB=7,RC=4,RD=2.5] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-3-0.tex new file mode 100644 index 00000000000..7280fbab946 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{brown}{orange} + \grBalaban[form=3,RA=7,RB=6.5,RC=5.6,RD=5.6,RE=4.6] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-4-0.tex new file mode 100644 index 00000000000..1dcae5cf4d5 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-2-4-0.tex @@ -0,0 +1,25 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[scale=.7] + \renewcommand*{\VertexInnerSep}{3pt} + \renewcommand*{\VertexLineWidth}{0.4pt} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{blue!50!black} + \grLCF[Math,RA=7]{% + 44,26,-47,-15,35,-39,11,-27,38,-37,43,14,28,51,-29,-16,41,-11,% + -26,15,22,-51,-35,36,52,-14,-33,-26,-46,52,26,16,43,33,-15,% + 17,-53,23,-42,-35,-28,30,-22, 45,-44,16,-38,-16,50,-55,20,28,% + -17,-43,47, 34,-26,-41,11,-36,-23,-16,41,17,-51,26,-33,47,17,% + -11,-20 ,-30,21,29,36,-43,-52,10,39,-28,-17,-52,51,26,37,-17,% + 10,-10,-45,-34,17,-26,27,-21,46,53,-10,29,-50,35,15,-47,-29,-41,% + 26,33,55,-17,42,-26,-36,16}{1} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-1-0.tex new file mode 100644 index 00000000000..28bcd3b3f33 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-1-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[node distance=4cm] + \grKonisberg + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-2-0.tex new file mode 100644 index 00000000000..1c140d89255 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-20-2-0.tex @@ -0,0 +1,33 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \renewcommand*{\VertexBallColor}{orange!50!red} + \renewcommand*{\EdgeDoubleDistance}{2pt} + \SetGraphUnit{4} + \GraphInit[vstyle=Shade] + \tikzset{LabelStyle/.style = {draw, + fill = yellow, + text = red}} + \Vertex{A} + \EA(A){B} + \EA(B){C} + {\SetGraphUnit{8} + \NO(B){D}} + \Edge[label=1](B)(D) + \tikzset{EdgeStyle/.append style = {bend left}} + \Edge[label=4](A)(B) + \Edge[label=5](B)(A) + \Edge[label=6](B)(C) + \Edge[label=7](C)(B) + \Edge[label=2](A)(D) + \Edge[label=3](D)(C) + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-0-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-0-0.tex new file mode 100644 index 00000000000..386b996553f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-0-0.tex @@ -0,0 +1,11 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-1-0.tex new file mode 100644 index 00000000000..bd00b63a4f8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-1-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \grLCF[prefix=a,RA=6]{-13,-9,7,-7,9,13}{5} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-2-0.tex new file mode 100644 index 00000000000..5b4f3141e3f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-21-2-0.tex @@ -0,0 +1,19 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCycle[prefix=a,RA=7]{10} + \EdgeInGraphMod{a}{10}{5} + \grEmptyCycle[prefix=b,RA=5]{10} + \grEmptyCycle[prefix=c,RA=3]{10} + \EdgeInGraphMod{c}{10}{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-1-0.tex new file mode 100644 index 00000000000..5038b00b0e2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-1-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grMcGee[Math,RA=6] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-2-0.tex new file mode 100644 index 00000000000..1e50d3d40e7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-2-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[Math,RA=6]{-12,-6,6,-12,7,-7,-12,6,-6,-12,7,-7}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-3-0.tex new file mode 100644 index 00000000000..51d446b8116 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-22-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[Math,RA=6]{-12,6,-7,-12,7,-8,11,-6,6,-11,8,% + -7,-12,7,-6,-12,7,-11,-8,7,-7,8,11,-7}{1} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-1-0.tex new file mode 100644 index 00000000000..d8d31518777 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-1-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetGraphArtColor{red}{olive} + \SetVertexNoLabel + \grMobiusKantor[RA=7] +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-2-0.tex new file mode 100644 index 00000000000..d05ad25be3c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-2-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=22.5] + \GraphInit[vstyle=Shade] + \SetGraphArtColor{red!50}{brown!50} + \SetVertexNoLabel + \grMobiusKantor[form=2,RA=7,RB=3] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-3-0.tex new file mode 100644 index 00000000000..9b3892a74d2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grMobiusKantor[form=3,RA=7,RB=2] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-4-0.tex new file mode 100644 index 00000000000..e9fcbbd8dcb --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-4-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grLCF[RA=7]{5,-5}{8} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-5-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-5-0.tex new file mode 100644 index 00000000000..7dddbf751c4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-5-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grGeneralizedPetersen[RA=7,RB=4]{8}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-6-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-6-0.tex new file mode 100644 index 00000000000..40ab948db1f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-6-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grMobiusLadder[RA=7,RB=2]{8}% + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-7-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-7-0.tex new file mode 100644 index 00000000000..f1f0448ac35 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-23-7-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grCirculant[RA=7]{16}{1,8}% +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-1-0.tex new file mode 100644 index 00000000000..b4185cf645a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-1-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \grPappus[RA=7] +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-2-0.tex new file mode 100644 index 00000000000..590ac78fcb9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-2-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPappus[form=2,RA=7,RB=5,RC=3] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-3-0.tex new file mode 100644 index 00000000000..d828fd4bb22 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-24-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{blue} + \grPappus[form=3,RA=7,RB=5,RC=2.5] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-1-0.tex new file mode 100644 index 00000000000..bb01c70ff82 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=1,RA=5,RB=3]% + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-2-0.tex new file mode 100644 index 00000000000..9b5b33350d4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-2-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=2,RA=7,RB=3]% +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-3-0.tex new file mode 100644 index 00000000000..ee2317b7c94 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{olive} + \grPetersen[form=3,RA=7]% +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-4-0.tex new file mode 100644 index 00000000000..71a2ed93981 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-4-0.tex @@ -0,0 +1,21 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} +\GraphInit[vstyle=Art]\SetGraphArtColor{white}{blue} + \begin{scope}[rotate=-90] \grCirculant[RA=1.5,prefix=a]{5}{2}\end{scope} + \begin{scope}[rotate=-18] \grEmptyCycle[RA=4,prefix=b]{5}{2} \end{scope} + \begin{scope}[rotate=18] \grCycle[RA=7,prefix=c]{5} \end{scope} + \EdgeIdentity{a}{b}{5} + \EdgeIdentity{b}{c}{5} + \EdgeDoubleMod{b}{5}{0}{1}{a}{5}{2}{1}{5} + \EdgeDoubleMod{c}{5}{0}{1}{b}{5}{1}{1}{5} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-5-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-5-0.tex new file mode 100644 index 00000000000..bd84e435833 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-5-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90,scale=.6] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{4pt} + \grGeneralizedPetersen[RA=5,RB=2]{5}{1} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-6-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-6-0.tex new file mode 100644 index 00000000000..4c83f7904ab --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-6-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{5}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-7-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-7-0.tex new file mode 100644 index 00000000000..09669b469f0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-7-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{6}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-8-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-8-0.tex new file mode 100644 index 00000000000..84fca5f6474 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-8-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \renewcommand*{\VertexInnerSep}{8pt} + \grGeneralizedPetersen[RA=7,RB=4]{7}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-9-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-9-0.tex new file mode 100644 index 00000000000..14cbf67b377 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-25-9-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \renewcommand*{\VertexInnerSep}{8pt} + \GraphInit[vstyle=Art]\SetGraphArtColor{red}{olive} + \grGeneralizedPetersen[RA=7,RB=4]{11}{5} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-1-0.tex new file mode 100644 index 00000000000..900f4816b64 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-1-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Shade] + \renewcommand*{\VertexInnerSep}{4pt} + \SetVertexNoLabel\SetGraphShadeColor{red!50}{black}{red} + \grTetrahedral[RA=5] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-10-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-10-0.tex new file mode 100644 index 00000000000..947532725c5 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-10-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{-4,-3,4}{6} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-11-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-11-0.tex new file mode 100644 index 00000000000..ead99f0ad26 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-11-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{-2,2,3}{6} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-12-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-12-0.tex new file mode 100644 index 00000000000..03df840244b --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-12-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18,scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grDodecahedral[RA=7,RB=4,RC=2,RD=1] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-13-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-13-0.tex new file mode 100644 index 00000000000..d9a593527ce --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-13-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCycle[RA=7,prefix=a]{10} + \grSQCycle[RA=4,prefix=b]{10} + \foreach \v in {0,...,9} + {\Edge(a\v)(b\v)} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-14-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-14-0.tex new file mode 100644 index 00000000000..2c0e1e8884c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-14-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{10,7,4,-4,-7,10,-4,7,-7,4}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-2-0.tex new file mode 100644 index 00000000000..11d26edb658 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-2-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18] + \renewcommand*{\VertexInnerSep}{8pt} + \GraphInit[vstyle=Art] + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{2,-2}{2} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-3-0.tex new file mode 100644 index 00000000000..f4ba7fe93a0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-3-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grSQCycle[RA=5]{6} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-4-0.tex new file mode 100644 index 00000000000..781f7c76eff --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-4-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCubicalGraph[RA=5,RB=2] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-5-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-5-0.tex new file mode 100644 index 00000000000..fa89a71cea9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-5-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCubicalGraph[form=2,RA=7,RB=4] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-6-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-6-0.tex new file mode 100644 index 00000000000..739c2e87baa --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-6-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=18] + \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grLCF[RA=7]{3,-3}{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-7-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-7-0.tex new file mode 100644 index 00000000000..44f280b936b --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-7-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.8] + \GraphInit[vstyle=Art]\renewcommand*{\VertexInnerSep}{4pt} + \SetGraphArtColor{red}{orange} + \grIcosahedral[RA=5,RB=1] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-8-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-8-0.tex new file mode 100644 index 00000000000..688cd51d4e2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-8-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=-30] + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grIcosahedral[form=2,RA=8,RB=2,RC=.8] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-9-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-9-0.tex new file mode 100644 index 00000000000..96af13b98de --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-26-9-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] \renewcommand*{\VertexInnerSep}{8pt} + \SetGraphArtColor{red!50}{orange} + \grIcosahedral[RA=1,RB=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-1-0.tex new file mode 100644 index 00000000000..a9a38247673 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{black}{gray} + \grRobertson[RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-2-0.tex new file mode 100644 index 00000000000..d633023fc9a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-2-0.tex @@ -0,0 +1,54 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.9] + \tikzstyle{TempEdgeStyle}= [thick,black,% + double = gray,% + double distance = 1.5pt]% + \SetVertexNoLabel + \renewcommand*{\VertexBigMinSize}{14pt} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \SetUpEdge[style = {thick,% + double = orange,% + double distance = 1pt}] + + \SetGraphShadeColor{gray}{black}{gray} + \tikzstyle{EdgeStyle} = [TempEdgeStyle] + \begin{scope}[rotate=-30] + \grEmptyCycle[RA=5.4]{3} + \end{scope} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=10] + \grCycle[prefix=b,RA=4]{12} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \grCirculant[prefix=c,RA=2]{4}{2} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left] + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right] + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3} + \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=60] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3} + \tikzstyle{EdgeStyle}=[TempEdgeStyle,in=-50,out=-120, + relative,looseness=2.5] + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-3-0.tex new file mode 100644 index 00000000000..3c65413dd29 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-3-0.tex @@ -0,0 +1,41 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[scale=1] + \GraphInit[vstyle=Art] + \SetGraphArtColor{gray}{red} + \begin{scope}[rotate=-30] + \grEmptyCycle[RA=5]{3} + \end{scope} + {\tikzset{EdgeStyle/.append style = {bend right=10}} + \grCycle[prefix=b,RA=3.5]{12}} + \grCirculant[prefix=c,RA=2]{4}{2} + {\tikzset{EdgeStyle/.append style = {bend left}} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{4}{3}{4}} + {\tikzset{EdgeStyle/.append style = {bend right}} + \EdgeDoubleMod{c}{4}{0}{1} + {b}{12}{8}{3}{4}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{11}{4}{3} + \EdgeDoubleMod{c}{4}{0}{1}% + {b}{12}{0}{3}{4} + {\tikzset{EdgeStyle/.append style = {bend left=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{8}{4}{3}} + {\tikzset{EdgeStyle/.append style = {bend right=60}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{2}{4}{3}} + {\tikzset{EdgeStyle/.append style = {in=-50,out=-120,% + relative,looseness=2.5}} + \EdgeDoubleMod{a}{3}{0}{1}% + {b}{12}{5}{4}{3}} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-4-0.tex new file mode 100644 index 00000000000..47e59758215 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-27-4-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90] + \GraphInit[vstyle=Art] + \grLCF[RA=6]{6,12}{15} + \EdgeInGraphMod{a}{30}{9}{1}{6} \EdgeInGraphMod*{a}{30}{15}{2}{6} + \EdgeInGraphMod*{a}{30}{9}{3}{6} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-28-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-28-1-0.tex new file mode 100644 index 00000000000..544c5bc8f0c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-28-1-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Art] + \tikzset{VertexStyle/.append style={minimum size=2pt}} + \SetGraphArtColor{blue}{darkgray} + \grTutteCoxeter +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-29-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-29-1-0.tex new file mode 100644 index 00000000000..ab8e9baade3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-29-1-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90,scale=.6] + \GraphInit[vstyle=Art] + \SetGraphArtColor{red}{blue} + \grWong[RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-1-0.tex new file mode 100644 index 00000000000..3adf1b23110 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-1-0.tex @@ -0,0 +1,19 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=2,RB=2,RS=3]{3}{2} +\end{tikzpicture}\hspace*{2cm} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=2,RB=2,RS=3]{3}{3} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-2-0.tex new file mode 100644 index 00000000000..64e9a64e8ff --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-2-0.tex @@ -0,0 +1,15 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=1.5] + \GraphInit[vstyle=Art] + \grCompleteBipartite[RA=3,RB=2,RS=5]{3}{5} +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-3-0.tex new file mode 100644 index 00000000000..f360ec4091e --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-3-3-0.tex @@ -0,0 +1,39 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{6}{1,3} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{8}{1,3} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{10}{1,3,5} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3]{12}{1,3,5} +\end{tikzpicture} + +\vspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3]{14}{1,3,5,7} +\end{tikzpicture}\hspace*{12pt} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3]{16}{1,3,5,7} +\end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-4-0-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-4-0-0.tex new file mode 100644 index 00000000000..e3e58b3ce11 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-4-0-0.tex @@ -0,0 +1,22 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[node distance=4cm] + \GraphInit[vstyle=Shade] + \Vertex{a0} + \NOEA(a0){a2} + \NOEA(a2){a4} + \NOWE(a0){a1} + \NOWE(a1){a3} + \Edges(a0,a1,a3) + \Edges(a0,a2,a4) + \Edge(a1)(a2) + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-1-0.tex new file mode 100644 index 00000000000..0bc97c46947 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-1-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \grCocktailParty[RA=3,RS=5]{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-2-0.tex new file mode 100644 index 00000000000..89fb40d5662 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-6-2-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \grCocktailParty[form=2,RA=4,RS=6]{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-1-0.tex new file mode 100644 index 00000000000..5b88ecb8d33 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-1-0.tex @@ -0,0 +1,22 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[rotate=90,scale=1] + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=5,prefix=a]{7} + \begin{scope}[rotate=-20]\grEmptyCycle[RA=4,prefix=b]{7}\end{scope} + \grCirculant[RA=3,prefix=c]{7}{2} + \grCirculant[RA=1.4,prefix=d]{7}{3} + \EdgeIdentity{a}{b}{7} + \EdgeIdentity{b}{c}{7} + \EdgeIdentity{b}{d}{7} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-2-0.tex new file mode 100644 index 00000000000..9cbbc3ddf0a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-2-0.tex @@ -0,0 +1,23 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=7,prefix=b]{24} + \grEmptyStar[RA=3,prefix=a]{4} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{0}{8}{2} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{7}{8}{2} + \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{18}{8}{2} + \EdgeDoubleMod{a}{4}{3}{0}{b}{24}{22}{8}{2} + \EdgeInGraphMod*{b}{24}{6}{5}{8} + \EdgeInGraphMod*{b}{24}{11}{1}{8} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-3-0.tex new file mode 100644 index 00000000000..f85bd2e7cae --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-3-0.tex @@ -0,0 +1,23 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{magenta}{gray} + \grCycle[RA=7,prefix=c]{7} + \grEmptyCycle[RA=6,prefix=b]{7} + \begin{scope}[rotate=12.85]\grEmptyCycle[RA=5,prefix=a]{14}\end{scope} + \EdgeIdentity{b}{c}{7} + \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{0}{2}{6} + \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{13}{2}{6} + \EdgeInGraphModLoop{a}{14}{4}{0}{0} + \EdgeInGraphModLoop{a}{14}{6}{1}{1} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-4-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-4-0.tex new file mode 100644 index 00000000000..0421c01f34b --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-4-0.tex @@ -0,0 +1,20 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture}[scale=3] + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{cyan} + \begin{scope}[rotate=5]\grCycle[RA=2.5,prefix=a]{10}\end{scope} + \begin{scope}[rotate=-10]\grCirculant[RA=1.8,prefix=b]{10}{5}\end{scope} + \begin{scope}[rotate=36]\grCirculant[RA=1.1,prefix=c]{10}{3}\end{scope} + \EdgeIdentity{a}{b}{10} + \EdgeIdentity{b}{c}{10} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-5-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-5-0.tex new file mode 100644 index 00000000000..60e847cab2b --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-7-5-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue}{darkgray} + \grLCF[RA=7]{-13,-9,7,-7,9,13}{5} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-1-0.tex new file mode 100644 index 00000000000..2387ea76251 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-1-0.tex @@ -0,0 +1,17 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture}[scale=.7] + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \SetGraphShadeColor{blue!50!black}{blue}{gray} + \grChvatal[RA=6,RB=2] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-2-0.tex new file mode 100644 index 00000000000..c58fb0cbf77 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-2-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue!50!black}{gray} + \grChvatal[form=2,RA=7,RB=4,RC=1.4] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-3-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-3-0.tex new file mode 100644 index 00000000000..f3af535ca9c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-8-3-0.tex @@ -0,0 +1,16 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + + \begin{tikzpicture} + \GraphInit[vstyle=Art] + \SetGraphArtColor{blue!50!black}{gray} + \grChvatal[form=3,RA=7] + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-1-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-1-0.tex new file mode 100644 index 00000000000..1b7ceb44286 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-1-0.tex @@ -0,0 +1,23 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} +\tikzstyle{VertexStyle} = [shape = circle, + shading = ball, + ball color = green, + minimum size = 24pt, + draw] +\tikzstyle{EdgeStyle} = [thick, + double = orange, + double distance = 1pt] +\SetVertexLabel\SetVertexMath +\grCrown[RA=3,RS=6]{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-2-0.tex b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-2-0.tex new file mode 100644 index 00000000000..1a0413e5d24 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/latex/tkzNamed-9-2-0.tex @@ -0,0 +1,14 @@ +% +% tkz-namedgraphs (27/05/2011) +% +% Coding (utf8) Creator (TeX) +% Author Alain Matthes +\input{tkzpreamblenamed.ltx} + +\begin{document} + +\begin{tikzpicture} + \grCrown[form=2,RA=4,RS=6]{4} + \end{tikzpicture} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/tkzpreamblenamed.ltx b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/tkzpreamblenamed.ltx new file mode 100644 index 00000000000..fb0fc3b909f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/NamedGraphs/examples/tkzpreamblenamed.ltx @@ -0,0 +1,3 @@ +\documentclass[border=3mm]{standalone} +\usepackage{tkz-berge} +
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/README.md b/Master/texmf-dist/doc/latex/tkz-berge/README.md new file mode 100644 index 00000000000..1946302786f --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/README.md @@ -0,0 +1,68 @@ +# tkz-berge — tools for classic graphs of graph theory + +Release 2.0 2021/01/20 + +## Description + +The package tkz-berge.sty is a collection of some useful macros if you want to + draw some classic graphs of the graph theory or to make others graphs. +The macros are designed to give math teachers (and students) easy access +at the programmation of drawing graphswith TikZ. I therefore hope that my + packages provide ideal tools for teachers wanting to offer their students fine documents of maths. +Some of graphs have names, sometimes inspired by th + +## Licence + +The scontents package may be modified and distributed under the terms and +conditions of the [LaTeX Project Public License](https://www.latex-project.org/lppl/), version 1.3c or greater. + + +## Requirements + +The package compiles with utf8, pdflatex and lualatex, loads and depends on updated versions of: +- [tkz-graph] +- [tikz](https://ctan.org/pkg/tikz) + +## Installation + +The package `tkz-berge` is present in TeXLive and MiKTeX, use the package +manager to install. + +You can experiment with the `tkz-berge` and `tkz-graph` packages by placing all of the +distribution files in the directory containing your current tex file. + + +## How to use it + +To use the package `tkz-berge`, place the following line in the preamble of +your LaTeX document: + +``` +\usepackage{tkz-berge} +``` +If you use the xcolor package, load that package before tkz-berge to avoid + package conflicts. + +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{tkz-berge} + +## Documentation + +The documentation is in english. +Documentation for `tkz-berge` is available on `CTAN`. + +## Examples + +All examples given in documentation will be stored on `CTAN` as standalone +files, ready for compilation. + +Other examples, in french, are on my site: [http://altermundus.fr](http://altermundus.fr) + +## History + +- 2.00 correction of bugs and new documentation +- 1.00 first version + +## Author + +Alain Matthes, 5 rue de Valence, Paris 75005, al (dot) ma (at) mac (dot) com diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-classic.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-classic.tex new file mode 100644 index 00000000000..cca3b768fe0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-classic.tex @@ -0,0 +1,616 @@ +\section{Classic Graphs} +%<––––––––––––––––––––––– graphes classiques –––––––––––––––––––––––––> +\subsubsection{Cycle graph} +\begin{NewMacroBox}{grCycle}{\oarg{local options}\var{order}} + +\medskip +\emph{A cycle graph $C_n$ is a graph on $n$ nodes containing a single cycle through all nodes. Cycle graphs can be generated using \tkzcname{grCycle} in the \tkzname{tkz-berge.sty} package. Special cases include the triangle graph and the square graph.} + +\medskip +External links : + +\medskip +\begin{itemize} + +\item \href{http://mathworld.wolfram.com/CycleGraph.html}% + {\textcolor{blue}{MathWorld - CycleGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + +\item \href{http://en.wikipedia.org/wiki/Cycle_graph}% + {\textcolor{blue}{Wikipedia}} + +\end{itemize} +\end{NewMacroBox} + +\subsubsection{Special cases : the triangle graph and the square graph} + + +\begin{center} +\begin{tkzexample}[small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grCycle[prefix=a,RA=3]{5} + \grCycle[x=4,y=3,prefix=b,RA=2]{3} + \grCycle[prefix=d,y=6,rotation=30,RA=2]{4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsubsection{Complete graph} +\begin{NewMacroBox}{grComplete}{\oarg{local options}\var{order}} + +\medskip +\emph{The more simple definition is "an undirected graph with an edge between every pair of vertices" or a complete graph is a simple graph in which each pair of graph vertices is connected by an edge. The complete graph with $n$ graph vertices is denoted $K_n$. This graph has $\frac{n(n-1)}{2}$ undirected edges.\\ +Geometrically, $K_3$ relates to a triangle,$ K_4$ a tetrahedron is the tetrahedral graph as well as the wheel graph , $K_5$ a pentachoron, etc \dots} + +\medskip +External links : + +\medskip +\begin{itemize} + +\item \href{http://en.wikipedia.org/wiki/Complete_graph}% + {\textcolor{blue}{Wikipedia}} + +\item \href{http://mathworld.wolfram.com/grComplete.html}% + {\textcolor{blue}{MathWorld - Complete graph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{itemize} +\end{NewMacroBox} + + +\subsubsection{Complete Graph order 4} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \renewcommand*{\VertexBallColor}{green!50!black} + \GraphInit[vstyle=Shade] + \grComplete[RA=5]{7} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\newpage\null + +\subsubsection{Complete Graph order 4} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \renewcommand*{\VertexBallColor}{green!50!black} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grComplete[RA=7]{16} +\end{tikzpicture} +\end{tkzexample} +\end{center} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{Circulant graph} +\begin{NewMacroBox}{grCirculant}{\oarg{local options}\var{order}} + +\medskip +\emph{The circulant graph is defined for any order $n$ at least 3, and every subset $L$ of integers which are less than or equal to $n/2$. A circulant graph is a graph in which the $i$th graph vertex is adjacent to the ($i+j$)th and ($i-j$)th graph vertices for each $j$ in a list $L$ . The circulant graphs with $L=\{1;\dots;[n/2]\}$ gives the complete graphs and the circulant graph with $L=\{1\}$ gives the cyclic graphs. The Möbius ladders are examples of circulant graphs.\\ + In graph theory, a graph whose adjacency matrix is circulant is called a circulant graph.\\ +The circulant graph on vertices on a list of nodes is implemented as \tkzcname{grCirculant} in the \tkzname{tkz-berge.sty} package.} + +\medskip +External links : + +\href{http://mathworld.wolfram.com/CirculantGraph.html}% + {\textcolor{blue}{MathWorld - CirculantGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} +\end{NewMacroBox} + +\tikzset{VertexStyle/.style = {shape = circle, + shading = ball, + ball color = green!40!black,% + minimum size = 16pt,% + draw}} +\SetUpEdge[style = {thick,% + double = orange,% + double distance = 1pt}] + +\SetVertexNoLabel +\tikzset{EdgeStyle/.style = {thick, + double= orange, + double distance = 1pt}} + +\subsubsection{Graph order 5 with L=\{1\}} + +This is a cycle graph. + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCirculant[RA=3]{5}{1}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Graph order 5 with L=\{2\}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCirculant[RA=3]{5}{2}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Graph order 5 with L=\{1,2\}} + +This graph is complete with an order $5$. + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCirculant[RA=3]{5}{1,2}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Graph order 10 with L=\{1,2,3,4,5\}} + +This graph is also complete + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCirculant[RA=4]{10}{1,2,3,4,5}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +It's interesting to remark that the numbers 3 and 10 are primer, so if $L=\{3\} $ the graph is containing an Eulerian circuit. + + +\subsubsection{Graph order 10 with L=\{3\}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCirculant[RA=4]{10}{3}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage\null +\tikzset{VertexStyle/.style = {shape = circle, + shading = ball, + ball color = gray!30,% + minimum size = 24pt,% + draw}} +\tikzset{EdgeStyle/.style = {thick,% + double = orange,% + double distance = 1pt}} +\SetVertexMath + +\subsubsection{Graph order 21 with L=\{1,3,10\}} + +\SetVertexNoLabel +\begin{tikzpicture} + \grCirculant[Math,RA=7]{21}{1,3,10} +\end{tikzpicture} +%<––––––––––––––––––––––––––– STAR –––––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{Star graph} + +\begin{NewMacroBox}{grStar}{\oarg{local options}\var{order}} + +\medskip +\emph{A star graph $S_n$ is a n-graph with one node having vertex degree $n-1$ and the other $n-1$ having vertex degree $1$. Star graphs can be generated using \tkzcname{grStar} in the \tkzname{tkz-berge.sty} package.} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/StarGraph.html}% + {\textcolor{blue}{MathWorld - StarGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + +\tikzset{VertexStyle/.style = {shape = circle, + shading = ball, + ball color = orange!40!,% + minimum size = 26pt,% + draw}} +\SetUpEdge[style={thick,% + double = orange,% + double distance = 1pt}] +\SetVertexNoLabel +\tikzset{EdgeStyle/.style = {thick, + double= orange, + double distance = 1pt }} + +\subsubsection{Star graph} +\begin{center} + \begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=30,scale=.8] + \grStar[RA=7]{8}% +\end{tikzpicture} +\end{tkzexample} +\end{center} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{Square graph} + + \begin{NewMacroBox}{grSQCycle}{\oarg{local options}\var{Number}} + +\medskip +\emph{A star graph $S_n$ is a n-graph with one node having vertex degree $n-1$ and the other $n-1$ having vertex degree $1$. Star graphs can be generated using \tkzcname{grStar} in the \tkzname{tkz-berge.sty} package.} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/SquareGraph.html}% + {\textcolor{blue}{MathWorld - SquareGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + +\subsubsection{Square Cycle graph} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.8] + \grSQCycle[RA=7]{10}% +\end{tikzpicture} +\end{tkzexample} +\end{center} +<–––––––––––––––––––––––––––– WHEEL –––––––––––––––––––––––––––––> +\newpage +\subsubsection{Wheel graph} + +\begin{NewMacroBox}{grWheel}{\oarg{local options}\var{Number}} + +\medskip +\emph{A wheel graph of order $n$ is a graph that contains a cycle of order $n-1$, and for which every vertex in the cycle is connected to one other vertex. The wheel can be defined as the graph , where is the singleton graph and is the cycle graph.} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/WheelGraph.html}% + {\textcolor{blue}{MathWorld - WheelGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + +\tikzset{VertexStyle/.style = {shape = circle, + shading = ball, + ball color = orange!40,% + minimum size = 24pt,% + draw}} +\SetUpEdge[style={thick,% + double = orange,% + double distance = 1pt}] + +\SetVertexNoLabel +\tikzset{EdgeStyle/.style = {thick,double= orange,double distance = 1pt}} + +\vfill +\subsubsection{Wheel graph} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=.8] + \grWheel[RA=7]{13}% +\end{tikzpicture} +\end{tkzexample} +\end{center} +%<–––––––––––––––––––––––––––– LADDER ––––––––––––––––––––––––––> +\newpage +\subsubsection{Ladder graph} + +\begin{NewMacroBox}{grLadder}{\oarg{local options}\var{Number}} + +\medskip +\begin{tabular}{llc} + \toprule +options & default & definition \\ +\midrule +\TOline{RA } { |4| } {radius circle n°1 } +\TOline{RS } { |0| } {distance between two lines } +\TOline{prefix } { |a| } {prefix for vertices } +\TOline{prefixx} { |b| } {prefix for vertices } +\TOline{Math } { |false|} {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{The ladder graph $L_n$ or cyclic ladder graph is equivalent to the grid graph having two rails and $n$ rungs between them.} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/LadderGraph.html}% + {\textcolor{blue}{MathWorld - LadderGraph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + +\vfill +\subsubsection{Ladder graph} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grLadder[RA=2,RS=4]{6}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill +%<––––––––––––––––––––––––––– Prism CYCLE LADDER –––––––––––––––––––––––> +\newpage +\subsubsection{Prism graph} + +\begin{NewMacroBox}{grPrism}{\oarg{local options}\var{Number}} + +\medskip +\begin{tabular}{llc} + \toprule +options & default & definition \\ +\midrule +\TOline{RA } { |4| } {radius circle n°1 } +\TOline{RB } { |3| } {radius circle n°2 } +\TOline{prefix } { |a| } {prefix for vertices } +\TOline{prefixx } { |b| } {prefix for vertices } +\TOline{Math } { |false|} {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{An $n$-prism graph has $2n$ nodes and $3n$ edges, and is equivalent to the generalized Petersen graph with arguments $n$ and $1$. For odd $n$, the $n$-prism is isomorphic to the circulant graph with an order $2n$ and with arguments $2$ and $n$.\\ +The 3-prism graph is the line graph of the complete bipartite graph with arguments $2$ and $3$ . The 4-prism graph is isomorphic with the cubical graph.} + + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/PrismGraph.html}% + {\textcolor{blue}{MathWorld - Prism Graph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + +\subsubsection{Cycle Ladder graph} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[rotate=15,scale=.7] + \grPrism[RA=6,RB=3]{6}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Cycle Ladder graph number 3} +\begin{center} +\begin{tkzexample}[] +\begin{tikzpicture}[scale=.7] + \grPrism[RA=6,RB=3]{3}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Cycle Ladder graph number 4} +\begin{center} +\begin{tkzexample}[] +\begin{tikzpicture}[scale=.7] + \grPrism[RA=6,RB=3]{4}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +%<––––––––––––––––––––––––––––– bipartite ––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{Complete Bipartite graph} + +\begin{NewMacroBox}{grCompleteBipartite}{\oarg{local options}\var{Number 1}\var{Number 2}} + +\medskip +\begin{tabular}{llc} + \toprule +options & default & definition \\ +\midrule +\TOline{RA }{|4| } {radius circle n°1} +\TOline{RB }{|3| } {radius circle n°2 } +\TOline{RS }{|1| } {distance between two lines } +\TOline{form }{|1| } {integer to obtain a new embedding of a graph} +\TOline{prefix }{|a| } {prefix for vertices } +\TOline{prefixx}{|b| } {prefix for vertices } +\TOline{Math }{|false| } {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{A complete bipartite graph is a bipartite graph (i.e., a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent) such that every pair of graph vertices in the two sets are adjacent.} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/CompleteBipartiteGraph.html}% + {\textcolor{blue}{MathWorld - CompleteBipartite Graph}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + + + +\subsubsection{Bipartite graph 1,5}\label{cl17} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCompleteBipartite[RA=4,RB=2.5,RS=4]{1}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Bipartite graph 3,5}\label{bi1} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCompleteBipartite[RA=4,RB=3,RS=6]{3}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{Triangular Grid graph} + + +\begin{NewMacroBox}{grTriangularGrid}{\oarg{local options}\var{Number}} + +\medskip +\begin{tabular}{llc} + \toprule +options & default & definition \\ +\bottomrule +\TOline{RA }{|4| }{distance between two vertices } +\TOline{form }{|1| }{integer to obtain a new embedding of a graph} +\TOline{prefix}{|a| }{prefix for vertices } +\TOline{Math }{|false|}{math mode } +\bottomrule +\end{tabular} + +\emph{Number=$n$ is the number of vertices of the first row then the graph order is $\dfrac{n(n-1)}{2} $. +There are three embeddings. You can use the option \tkzname{form} with an integer between $1$ and $3$.} +\end{NewMacroBox} + +\medskip + + +\subsubsection{n=8 order=28 form 1}\label{cl18a} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexLabel + \grTriangularGrid[prefix=G,Math,RA=1.5]{8}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{n=6 order=15 form 2} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grTriangularGrid[RA=2,form=2]{6}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{n=6 order=15 form 3} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetVertexNoLabel + \grTriangularGrid[RA=2,form=3]{6}% +\end{tikzpicture} +\end{tkzexample} +\end{center} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newpage +\subsubsection{LCF Lederberg-Coxeter-Fruchte} + +\begin{NewMacroBox}{grLCF}{\oarg{RA=\meta{Number}} \var{List of numbers} \var{Number}} +\emph{LCF = Lederberg-Coxeter-Fruchte (see the link below for some examples).} + +\medskip +External links : + +\medskip +\begin{itemize} +\item \href{http://mathworld.wolfram.com/LCFNotation.html}% + {\textcolor{blue}{MathWorld-LCF Notation}} by % + \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{Weisstein}} +\end{itemize} +\end{NewMacroBox} + + +\subsubsection{\texorpdfstring{$\big[2,-2\big]^2$}{}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \grLCF[RA=5]{2,-2}{2}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{\texorpdfstring{$\big[3,-3\big]^4$}{}} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \grLCF[RA=5]{3,-3}{4}% +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Ljubljana graph} +From Wikipedia \url{http://en.wikipedia.org/wiki/Ljubljana_graph} + +\emph{The Ljubljana graph was first published in 1993 by Brouwer, Dejter and Thomassen. +In 1972, Bouwer was already talking of a 112-vertices edge- but not vertex-transitive cubic graph found by R. M. Foster, but unpublished. Conder, Malnič, Marušič, Pisanski and Potočnik rediscovered this 112-vertices graph in 2002 and named it the Ljubljana graph after the capital of Slovenia. They proved that it was the unique 112-vertices edge- but not vertex-transitive cubic graph and therefore that was the graph found by Foster.} + +It can be represented in LCF notation as : + +\[ +\begin{array}{l} +\Big[ 47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15, -49, 33, 39, -35, -21, 17,\\ -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21, 31, -51, -25, 23, 9, -17, 51, 35, -29, 21,\\ -51, -39, 33, -9, -51, 51, -47, -33, 19, 51, -21,29, 21, -31, -39\Big]^2 +\end{array} +\] + + + \begin{center} +\begin{tikzpicture} +\GraphInit[vstyle=Art] +\SetGraphArtColor{black!50}{darkgray} +\tikzset{VertexStyle/.append style = { + minimum size = 3pt}} + \grLCF[RA=7]{47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15, -49, 33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21, 31, -51, -25, 23, 9, -17, 51, 35, -29, 21, -51, -39, 33, -9, -51, 51, -47, -33, 19, 51, -21, 29, 21, -31, -39}{2}% +\end{tikzpicture} +\end{center} + +\begin{tkzexample}[code only] +\GraphInit[vstyle=Art] +\SetGraphArtColor{black!50}{darkgray} +\tikzset{VertexStyle/.append style = { + minimum size = 3pt}} +\begin{tikzpicture}% + \grLCF[RA=7]{47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15,% + -49, 33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21,% + 31, -51, -25, 23, 9, -17, 51, 35, -29, 21, -51, -39, 33, -9, -51, 51, -47,% + -33, 19, 51, -21, 29, 21, -31, -39}{2}% +\end{tikzpicture} +\end{tkzexample} +\vfill +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros-e.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros-e.tex new file mode 100644 index 00000000000..94f1f8aa183 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros-e.tex @@ -0,0 +1,457 @@ +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\section{Macros and Edges in a graph} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\subsection{Edge in a graph from one vertex \tkzcname{EdgeInGraphFromOneToComp}} + +\begin{NewMacroBox}{EdgeInGraphFromOneToComp}{\oarg{local options}\var{prefix}\var{order}\var{from}} + +\begin{tabular}{llc} +\hline +Arguments & & Definition \\ +\midrule +\TAline{order} {}{order of the graph} +\bottomrule +\end{tabular} + +\medskip +\begin{tabular}{llc} +\midrule +options & default & definition \\ +\midrule +\TOline{RA} {4} { radius circle} +\TOline{prefix} {a} {prefix for vertices } +\TOline{Math} {false} {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{This macro works on an unique graph. |from| is integer. |EdgeInGraph| designs a macro that works only in a graph defined by a prefix. The result is some edges between the vertex |from| and the others vertices. } +\end{NewMacroBox} + + + + + +\subsubsection{Empty Cycle} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=4,prefix=a]{8}% + \EdgeInGraphFromOneToComp{a}{8}{3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill +\newpage +\subsection{Edges in a graph - a loop \tkzcname{EdgeInGraphLoop}}% +\begin{NewMacroBox}{EdgeInGraphLoop}{\var{prefix}\var{order}} +\emph{This macro is useful with vertices on a circle . |order| in an integer.} +\end{NewMacroBox} + + +\subsubsection{Empty Cycle} +\begin{center} + \begin{tkzexample}[very small] + \begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=2,prefix=a]{8}% + \EdgeInGraphLoop{a}{8} + \end{tikzpicture}\end{tkzexample} +\end{center} + +\subsubsection{Empty Cycle} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture}[node distance=4cm] + \GraphInit[vstyle=Shade] + \Vertices{square}{a0,a1,a2,a3} + \EdgeInGraphLoop{a}{4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges in a graph - a loop \tkzcname{EdgeInGraphLoop*}} +\begin{NewMacroBox}{EdgeInGraphLoop*}{\var{prefix}\var{order}} + +\medskip +\emph{Not exactly a loop, there is no edge between the first and the last vertex.} +\end{NewMacroBox} + +\subsubsection{Empty Cycle} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grEmptyCycle[RA=4,prefix=a]{8}% + \EdgeInGraphLoop*{a}{8} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Path} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \grEmptyPath[prefix=h,RA=2,RS=2]{6} + \EdgeInGraphLoop*{h}{6} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill +\newpage +\subsection{Sequence of edges in a graph \tkzcname{EdgeInGraphSeq}} +\begin{NewMacroBox}{EdgeInGraphSeq}{\var{prefix}\var{start}\var{end}} + +\medskip +\emph{This macro gives a sequence of edges between |start| and |end|.\\ +|start| and |end| are two integers. } +\end{NewMacroBox} + +\subsubsection{EdgeInGraphSeq} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=2,prefix=a]{8}% + \EdgeInGraphSeq{a}{2}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges in a graph \tkzcname{EdgeInGraphMod}} +\begin{NewMacroBox}{EdgeInGraphMod}{\var{prefix}\var{order}\var{add}} + +\medskip +\emph{This macro works on an unique graph. Edges between $v_i$ and $v_j$ with $i$ in $0,...,(\text{\#2}-1)$ and $j=\text{Mod(i+\#3,\#2)}$.\\ +\#2 = |order| and \#3 = |add|.\\ +|Mod| is like |mod| but the result is a positive integer. } +\end{NewMacroBox} + +\subsubsection{EdgeInGraphMod} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=2,prefix=a]{8}% + \EdgeInGraphMod{a}{8}{2} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{EdgeInGraphMod 2} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=3,prefix=a]{13}% + \EdgeInGraphMod{a}{13}{3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges in a graph \tkzcname{EdgeInGraphMod*}} +\begin{NewMacroBox}{EdgeInGraphMod*}{\var{prefix}\var{order}\var{add}\var{start}\var{step}} + +\medskip +\emph{Edges between $v_i$ and $v_j$ with $i$ in $\#4,\#4+\#5,...,(\text{\#2}-1)$ and $j=\text{Mod(i+\#3,\#2)}$}\\ +\#2 = |order|, \#3 = |add|, \#4 = |start|, \#5 = |step|.\\ +\end{NewMacroBox} + +\subsubsection{EdgeInGraphMod*} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=a]{17}% + \EdgeInGraphMod*{a}{17}{5}{1}{2} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges in a graph \tkzcname{EdgeInGraphModLoop}} +\begin{NewMacroBox}{EdgeInGraphModLoop}{\var{prefix}\var{order}\var{add}\var{start}} + +\medskip +\emph{ |order|, |add| and |start| are integers.\\ +Edges between $v_i$ and $v_j$ with $i$ from $\#4$, $j=\text{Mod(i+\#3,\#2)}$ and then $i=j$ until $j=\#4$\\ +\#2 = |order|, \#3 = |add| and \#4 = |start|.} +\end{NewMacroBox} + +\subsubsection{EdgeInGraphModLoop} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=4]{7} + \EdgeInGraphModLoop{a}{7}{2}{1} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{EdgeInGraphModLoop} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=4]{8} + \EdgeInGraphModLoop{a}{8}{2}{1} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage +\subsection{Edges between two graphs with the same order \tkzcname{EdgeIdentity}} + +\begin{NewMacroBox}{EdgeIdentity}{\var{prefix1}\var{prefix2}\var{order}} + +\medskip +\emph{|order| is an integer. This macro gives edges between two graphs.\\ +Edges between $v_i$ and $v_j$ with $i=j$ in $0,...,(\text{\#3}-1)$.\\ +\#3 = |order|.\\} +\end{NewMacroBox} + +\subsubsection{EdgeIdentity} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=v,RA=3]{5} + \grEmptyCycle[prefix=w,RA=1]{5} + \EdgeIdentity{v}{w}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill +\newpage +\subsection{Edges between two graphs with the same order \tkzcname{EdgeIdentity*}} + +\begin{NewMacroBox}{EdgeIdentity*}{\var{prefix1}\var{prefix2}\var{list}} + +\medskip +\emph{|list| is a list of integers. This macro gives edges between two graphs.\\ +Edges between $v_i$ and $v_j$ with $i=j$ in |list|.\\} + +\end{NewMacroBox} + +\subsubsection{EdgeIdentity*} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \begin{scope}[rotate=30] + \grEmptyCycle[RA=3,prefix=a]{5}% + \end{scope} + \grEmptyCycle[RA=5,prefix=b]{5}% + \EdgeIdentity*{a}{b}{0,...,4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{EdgeIdentity*} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \begin{scope}[rotate=30] + \grEmptyCycle[RA=3,prefix=a]{5}% + \end{scope} + \grEmptyCycle[RA=5,prefix=b]{5}% + \EdgeIdentity*{a}{b}{0,2,4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeFromOneToAll}} +\begin{NewMacroBox}{EdgeFromOneToAll}{\var{prefix1}\var{prefix2}\var{from}\var{order}} + +\medskip +\emph{The graphs must to have the same order. |from| and |order| are integers.} +\end{NewMacroBox} + +\subsubsection{EdgeFromOneToAll} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grPath[form=1,RA=2,RS=0]{5} + \grPath[form=1,prefix=b,RA=2,RS=4]{5} + \EdgeFromOneToAll{a}{b}{1}{5} +\end{tikzpicture}\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeFromOneToSeq}} +\begin{NewMacroBox}{EdgeFromOneToSeq}{\var{prefix1}\var{prefix2}\var{from}\var{start}\var{end}} + +\medskip +\emph{|from|, |start| and |end| are integers. This macro builds edges between the vertex with an indice |from| through the vertices with an indice in the sequence |start|,...,|end|.} +\end{NewMacroBox} + +\subsubsection{EdgeFromOneToSeq} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grPath[form=1,RA=2,RS=0]{5} + \grPath[form=1,prefix=b,RA=2,RS=4]{5} + \EdgeFromOneToSeq{a}{b}{1}{2}{4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeFromOneToSel}} +\begin{NewMacroBox}{EdgeFromOneToSel}{\var{prefix1}\var{prefix2}\var{from}\var{list}} + +\medskip +\emph{This macro builds edges between the vertex with an indice |from| through the vertices with an indice in the list |list|.} +\end{NewMacroBox} + + +\subsubsection{EdgeFromOneToSel} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grPath[form=1,RA=2]{5} + \grPath[form=1,prefix=b,RA=2,RS=4]{5} + \EdgeFromOneToSel{a}{b}{1}{0,2,4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeFromOneToComp}} +\begin{NewMacroBox}{EdgeFromOneToComp}{\var{prefix1}\var{prefix2}\var{from}\var{order2}} + +\medskip +\emph{This macro builds edges between the vertex with an indice |from| through all the vertices of the second graph, except the vertex with an indice |from|.} +\end{NewMacroBox} + +\subsubsection{EdgeFromOneToComp} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grPath[form=1,RA=2,RS=0]{5} + \grPath[form=1,prefix=b,RA=2,RS=4]{5} + \EdgeFromOneToComp{a}{b}{2}{3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeMod}}% +\begin{NewMacroBox}{EdgeMod}{\var{prefix1}\var{prefix2}\var{order}\var{step}} + +\medskip +\emph{This macro works on two graphs with the same order. We get edges between $v_i$ and $v_j$ with $i$ in $0,...,(\text{\#2}-1)$ and $j=\text{Mod(i+\#4,\#3)}$.\\ +\#3 = |order| and \#4 = |step|.} +\end{NewMacroBox} + +\subsubsection{EdgeMod} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=a,RA=6]{9} + \grEmptyCycle[prefix=b,RA=3]{9} + \EdgeMod{a}{b}{9}{1} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeMod*}}% +\begin{NewMacroBox}{EdgeMod*}{\var{prefix1}\var{prefix2}\var{order}\var{step1}\var{step2}} + +\medskip +\emph{This macro works on two graphs with the same order. We get edges between $v_i$ and $v_j$ with $i$ in $0,...,(\text{\#3}-1)$ with a step $\text{\#5}$ and $j=\text{Mod(i+\#4,\#3)}$.\\ +\#3 = |order| , \#4 = |step1| and \#5 = |step2|.} +\end{NewMacroBox} + + +\subsubsection{\tkzcname{EdgeMod*} }%with |step1|=1 and |step2|=2 +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=a,RA=6]{8} + \grEmptyCycle[prefix=b,RA=4]{8} + \EdgeMod*{a}{b}{8}{1}{2} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{EdgeMod* }%with |step1|=2 and |step2|=1 +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=a,RA=6]{8} + \grEmptyCycle[prefix=b,RA=2]{8} + \EdgeMod*{a}{b}{8}{1}{1} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{Edges between two graphs \tkzcname{EdgeDoubleMod}}% +\begin{NewMacroBox}{EdgeDoubleMod}{\var{prefix1}\var{nb}\var{nb}\var{nb}\var{prefix2}\var{nb}\var{nb}\var{nb}\var{end}} + +For the first node, the numbers are : +\var{order1}\var{start1}\var{add1} + +\medskip +For the second node, the numbers are : +\var{order2}\var{start2}\var{add2}\var{end} + +\medskip +\emph{Edges between $v_i$ and $v_j$ with $i=\text{Mod(\#3+(\#4*k),\#2)}$ and j=$\text{Mod(\#7+(\#8*k),\#6)}$ $k$ is an integer from $0$ to |end|.\\ +\#2 = |order1|, \#3 = |start1| and \#4 = |add1|.\\ +\#6 = |order2|, \#7 = |start2| and \#8 = |add2|.} +\end{NewMacroBox} + + +\subsubsection{EdgeDoubleMod} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \begin{scope}[rotate=-90] + \grEmptyCycle[RA=2,prefix=a]{5} + \end{scope} + \begin{scope}[rotate=-18] + \grEmptyCycle[RA=4,prefix=b]{5} + \end{scope} + \EdgeDoubleMod{b}{5}{0}{1}% + {a}{5}{2}{1}{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{EdgeDoubleMod with two graphs and different orders} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=a,RA=5]{10} + \grEmptyCycle[prefix=b,RA=7]{20} + \EdgeDoubleMod{a}{10}{0}{1}% + {b}{20}{0}{2}{10} +\end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros.tex new file mode 100644 index 00000000000..5a3ded84cb1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-macros.tex @@ -0,0 +1,326 @@ +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\section{Macros and Vertices} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\subsection{\tkzcname{grEmptyCycle}} + +\begin{NewMacroBox}{grEmptyCycle}{\oarg{local options}\var{order}} +\begin{tabular}{llc} +Arguments & & Definition \\ +\midrule +\TAline{order} {}{order of the graph} +\bottomrule +\end{tabular} + +\medskip +\begin{tabular}{llc} + +Options & default & definition \\ +\midrule +\TOline{RA} {4} { radius circle} +\TOline{prefix} {a} {prefix for vertices } +\TOline{Math} {false} {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{The number of nodes in a graph is called its order. The argument "order" is an integer superior to $1$. |RA| defines the radius of the circle.} +\end{NewMacroBox} + + +\bigskip +\subsubsection{Empty Cycle} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=1.5]{3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Cycle and \tkzcname{SetVertexNoLabel}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \SetVertexNoLabel + \GraphInit[vstyle=Shade] + \grEmptyCycle[RA=1.5]{2} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Cycle and \tkzname{Math}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \grEmptyCycle[Math,RA=1.5]{4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Empty Cycle, \tkzcname{SetVertexMath} and \tkzname{prefix}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \SetVertexMath + \GraphInit[vstyle=Shade] + \grEmptyCycle[prefix=N,RA=1.5]{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Cycle and Classic style} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \SetVertexMath + \GraphInit[vstyle=Classic] + \grEmptyCycle[RA=1.5]{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Cycle and Simple style} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Simple] + \grEmptyCycle[RA=1.5]{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\newpage +\subsection{\tkzcname{grEmptyPath}} +\begin{NewMacroBox}{grEmptyPath}{\oarg{local options}\var{order}} +\begin{tabular}{llc} +\hline +Arguments & & Definition \\ +\midrule +\TAline{order} {}{order of the graph} +\bottomrule +\end{tabular} + +\medskip +\begin{tabular}{>{\color{green!50!black}}lllc} + \toprule +options & default & definition \\ +\midrule +\TOline{RA} {4 cm}{ distance between two vertices} +\TOline{RS} {? cm}{ distance between the first line and the new one} \\ +\TOline{prefix} {a} {prefix for vertices } +\TOline{Math} {false} {math mode } +\bottomrule +\end{tabular} + +\medskip +\emph{|Order| is the number of nodes. |RA| defines the radius of the circle. |RS| defines the distance between the graph and the baseline.} + +\end{NewMacroBox} + +\bigskip +\tikzset{VertexStyle/.style = {shape = circle,% + shading = ball,% + ball color = green!30, + minimum size = 24pt, + draw}} +\tikzset{EdgeStyle= {color=red!30, + double= green!50!black, + double distance = 2pt}} +\SetVertexLabel +\SetVertexMath +\subsubsection{Empty Path, \tkzname{RA} and \tkzname{Math}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \grEmptyPath[Math,RA=2]{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Path, \tkzname{RA} and \tkzname{prefix}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \grEmptyPath[prefix=h,RA=2]{6} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\subsubsection{Empty Path, vertical path with \tkzname{form=2}} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \grEmptyPath[form=2,prefix=v,RA=2]{3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\subsubsection{Two Empty Paths} +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \grEmptyPath[Math,prefix=p,RA=2,RS=0]{5} + \grEmptyPath[Math,prefix=q,RA=2,RS=3]{5} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grEmptyPath[Math,prefix=p,RA=2,RS=0,form=2]{5} + \grEmptyPath[Math,prefix=q,RA=2,RS=4,form=2]{5} +\end{tikzpicture} +\end{tkzexample} + \end{center} + +\subsubsection{How to move a graph ?} + +\begin{center} +\begin{tkzexample}[very small] +\begin{tikzpicture} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{blue!60!black!30}{blue}{white} + \grPath[Math,prefix=u,RA=2,RS=0]{4} + \grPath[Math,prefix=v,RA=2,RS=3]{4} + \begin{scope}[xshift=1 cm] + \grPath[Math,prefix=t,RA=2,RS=5]{4} + \end{scope} + \begin{scope}[shift={(4 cm,8cm)}] + \grPath[Math,prefix=x,RA=2,RS=0]{4} + \end{scope} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +% \newpage +% \subsection{Empty Star} +% \begin{NewMacroBox}{grEmptyStar}{\oarg{local options}\var{order}} +% \begin{tabular}{llc} +% \toprule +% Arguments & & Definition \\ +% \midrule +% \TAline{order} {}{order of the graph} +% \bottomrule +% \end{tabular} +% +% \medskip +% \begin{tabular}{>{\color{green!50!black}}lllc} +% \toprule +% options & default & definition \\ +% \midrule +% \TOline{RA} {4 cm}{ radius circle} +% \TOline{prefix} {a} {prefix for vertices } +% \TOline{Math} {false} {math mode } +% \bottomrule +% \end{tabular} +% +% \medskip +% \emph{|RA| defines the radius of the circle. |order| is an integer and it's the order of the graph.} +% \end{NewMacroBox} +% +% \bigskip +% \subsubsection{Empty Star} +% \begin{center} +% \begin{tkzexample}[very small] +% \begin{tikzpicture} +% \SetVertexMath +% \grEmptyStar[prefix=s,RA=3]{6} +% \end{tikzpicture} +% \end{tkzexample} +% \end{center} +% +% \newpage +% \subsection{Empty Grid} +% \begin{NewMacroBox}{grEmptyGrid}{\oarg{local options}\var{c}\var{r}} +% \begin{tabular}{llc} +% \toprule +% Arguments & & Definition \\ +% \midrule +% \TAline{r} {}{number of rows} +% \TAline{c} {} {number of columns} +% \bottomrule +% \end{tabular} +% +% \medskip +% \begin{tabular}{llc} +% \toprule +% options & default & definition \\ +% \midrule +% \TOline{RA} {4 cm}{ distance between two columns } +% \TOline{RB} {3 cm} {distance between two rows } +% \TOline{prefix} {3 cm} {distance between two rows } +% \TOline{Math} {false} {math mode } +% \bottomrule +% \end{tabular} +% +% \medskip +% \emph{|c| and |r| are integers.} +% +% \end{NewMacroBox} +% +% \bigskip +% \subsubsection{Prefix} +% \begin{center} +% \begin{tkzexample}[very small] +% \begin{tikzpicture} +% \tikzset{VertexStyle/.style ={shape = circle, +% shading = ball, +% ball color = Blue!60,% +% minimum size = 24pt,% +% draw}} +% \SetVertexMath +% \grEmptyGrid[prefix=G,RA=2,RB=4]{5}{3} +% \end{tikzpicture}\end{tkzexample} +% \end{center} +% +% \newpage +% \subsection{Empty Ladder} +% \begin{NewMacroBox}{grEmptyLadder}{\oarg{local options}\var{c}} +% \begin{tabular}{llc} +% \toprule +% Arguments & & Definition \\ +% \midrule +% \TAline{c} {}{number of columns.} +% \bottomrule +% \end{tabular} +% +% \medskip +% \begin{tabular}{llc} +% options & default & definition \\ +% \midrule +% \TOline{RA} {4 cm}{ distance between two columns } +% \TOline{RB} {3 cm}{ distance between two rows } +% \TOline{prefix} {a} {prefix for vertices } +% \TOline{prefix} {b} {prefix for vertices } +% \TOline{Math} {false} {math mode } +% \bottomrule +% \end{tabular} +% +% \medskip +% \emph{ |c| is an integer. There are only two rows with different prefix.} +% \end{NewMacroBox} +% +% \bigskip +% \subsubsection{Empty Ladder} +% \begin{center} +% \begin{tkzexample}[very small] +% \begin{tikzpicture} +% \tikzset{VertexStyle/.style ={shape = diamond, +% shading = ball, +% ball color = yellow!60,% +% minimum size = 24pt,% +% draw}} +% \SetVertexMath +% \grEmptyLadder[RA=2,RB=4]{5} +% \end{tikzpicture} +% \end{tkzexample} +% \end{center} + +\endinput + + diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-main.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-main.tex new file mode 100644 index 00000000000..5ad81802dcc --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-main.tex @@ -0,0 +1,270 @@ +% encoding : utf8 +% tkz-berge.tex +% Created by Alain Matthes on 2008-01-19. +% Copyright (C) 2009 Alain Matthes +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License , either version 1.3 +% of this license or (at your option) any later version and/or +% 2. under the GNU Public License. +% +% See the file doc/generic/pgf/licenses/LICENSE for more details.% +% See http://www.latex-project.org/lppl.txt for details. +% +% +% ``tkzdoc-berge-us'' is the english doc of tkz-berge +% +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% tkz-berge.sty encodage : utf8 % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% Créé par Alain Matthes le 19/02/2007 % +% Copyright (c) 2006 __Collège Sévigné__ All rights reserved. % +% version : 2.7 c % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Fichier .tex de présentation du package tkz-graph.sty +% d'après le code de DTK. + +\documentclass[DIV = 14, + fontsize = 10, + headinclude = false, + footinclude = false, + index = totoc, + twoside, + headings = small]{tkz-doc} +\usepackage{etoc} +\gdef\tkznameofpack{tkz-berge} +\gdef\tkzversionofpack{v 1.00 c} +\gdef\tkzdateofpack{2011/05/25} +\gdef\tkznameofdoc{doc-tkz-berge} +\gdef\tkzversionofdoc{v 1.00 c} +\gdef\tkzdateofdoc{2011/05/25} +\gdef\tkzauthorofpack{Alain Matthes} +\gdef\tkzadressofauthor{} +\gdef\tkznamecollection{AlterMundus} +\gdef\tkzurlauthor{http://altermundus.fr} +\gdef\tkzengine{lualatex} +\gdef\tkzurlauthorcom{http://altermundus.fr} + +% -- Packages --------------------------------------------------- +\usepackage[dvipsnames,svgnames]{xcolor} +\usepackage{calc} +\usepackage{tkz-berge} +\usetikzlibrary{calc,positioning,shapes} +\usepackage[colorlinks,pdfencoding=auto]{hyperref} +\hypersetup{ + linkcolor=Gray, + citecolor=Green, + filecolor=Mulberry, + urlcolor=NavyBlue, + menucolor=Gray, + runcolor=Mulberry, + linkbordercolor=Gray, + citebordercolor=Green, + filebordercolor=Mulberry, + urlbordercolor=NavyBlue, + menubordercolor=Gray, + runbordercolor=Mulberry, + pdfsubject={Euclidean Geometry}, + pdfauthor={\tkzauthorofpack}, + pdftitle={\tkznameofpack}, + pdfcreator={\tkzengine} +} +\usepackage{tkzexample} +\usepackage{fontspec} +\setmainfont{texgyrepagella}% + [Extension = .otf , + UprightFont = *-regular, + ItalicFont = *-italic, + BoldFont = *-bold, + BoldItalicFont = *-bolditalic] +\setsansfont{texgyreheros}[ + Extension = .otf, + UprightFont = *-regular , + ItalicFont = *-italic , + BoldFont = *-bold , + BoldItalicFont = *-bolditalic , +] + +\setmonofont{lmmono10-regular.otf}[ + Numbers={Lining,SlashedZero}, + ItalicFont=lmmonoslant10-regular.otf, + BoldFont=lmmonolt10-bold.otf, + BoldItalicFont=lmmonolt10-boldoblique.otf, +] +\newfontfamily\ttcondensed{lmmonoltcond10-regular.otf} +%% (La)TeX font-related declarations: +\linespread{1.05} % Pagella needs more space between lines + +\usepackage{unicode-math} +\usepackage{fourier-otf,zorna} +\usepackage{datetime,multicol,lscape} +\usepackage[french]{babel} +\usepackage[autolanguage]{numprint} +\usepackage{microtype} +\usepackage{array,multirow,multido,booktabs} +\usepackage{shortvrb,fancyvrb} +\usepackage{fancybox} +\usepackage{stmaryrd} +\usepackage{xkeyval,array} +\usepackage[weather]{ifsym} +\usepackage[format=hang,margin=10pt]{caption} +\usepackage{multicol} +\usepackage{makeidx} +\makeindex + +\title{The package : tkz-berge.sty} +\author{Alain Matthes} + +\AtBeginDocument{\MakeShortVerb{\|}} + + + +\begin{document} + +\parindent=0pt +\author{\tkzauthorofpack} +\title{\tkznameofpack} +\date{\today} +\clearpage +\thispagestyle{empty} +\maketitle + +\clearpage + +\tkzSetUpColors[background=white,text=darkgray] + +\let\rmfamily\ttfamily + +\nameoffile{\tkznameofpack} +\defoffile{The package \tkzname{\tkznameofpack} is a collection of some useful macros if you want to draw some classic graphs of the graph theory or to make others graphs. The kind of graphs that I will present, are sometimes called combinatorial graphs to distinguish them from the graphs of functions. Often, the word graph is short for graph of a function. A combinatorial graph is a very simple structure, a bunch of dots, some of which are connected by lines. Some of graphs have names, sometimes inspired by the graph's topology, and sometimes after their discoverer.\hfil\break +Why tkz-berge.sty ?\hfil\break +Claude Berge (1926 – 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory. He played a major role in the renaissance of combinatorics and he is remembered for his famous conjecture on perfect graphs, solved some months after his death.} + +\presentation + +\vfill +\lefthand\ Firstly, I would like to thank \textbf{Till Tantau} for the beautiful LATEX package, namely TikZ. + +\lefthand I am grateful to \textbf{Michel Bovani} for providing the \tkzname{fourier} font. + +\lefthand\ I received much valuable advice and guidance on Graph Theory from \textbf{Rafael Villarroel}\\ \url{http://graphtheoryinlatex.blogspot.com/}. + +\lefthand\ The names of graphs can be found here \href{http://mathworld.wolfram.com/topics/SimpleGraphs.html}% + {\textcolor{blue}{MathWorld - SimpleGraphs}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% + {\textcolor{blue}{E.Weisstein}} + + +\vspace{1cm} +Please report typos or any other comments to this documentation to \href{mailto:al.ma@mac.com}{\textcolor{blue}{Alain Matthes}} +This file can be redistributed and/or modified under the terms of the LATEX +Project Public License Distributed from CTAN archives in directory \url{CTAN:// +macros/latex/base/lppl.txt}. + +\clearpage +\tableofcontents +\clearpage + +\newpage +List of the main macros : + +\medskip + +\begin{multicols}{2} + \begin{itemize} + \item \tkzcname{grEmptyCycle} + \item \tkzcname{grEmptyPath} + \item \tkzcname{grEmptyStar} + \item \tkzcname{grEmptyGrid} + \item \tkzcname{grEmptyLadder} + \item \tkzcname{EdgeInGraphFromOneToComp} + \item \tkzcname{EdgeInGraphLoop} + \item \tkzcname{EdgeInGraphSeq} + \item \tkzcname{EdgeInGraphMod} + \item \tkzcname{EdgeInGraphMod*} + \item \tkzcname{grCompleteBipartite} + \item \tkzcname{EdgeInGraphModLoop} + \item \tkzcname{EdgeIdentity} + \item \tkzcname{EdgeIdentity*} + \item \tkzcname{EdgeFromOneToAll} + \item \tkzcname{EdgeFromOneToSeq} + \item \tkzcname{EdgeFromOneToSel} + \item \tkzcname{EdgeFromOneToComp} + \item \tkzcname{EdgeMod} + \item \tkzcname{EdgeMod*} + \item \tkzcname{EdgeDoubleMod} + \item \tkzcname{grPath} + \item \tkzcname{grCycle} + \item \tkzcname{grComplete} + \item \tkzcname{grCirculant} + \item \tkzcname{grStar} + \item \tkzcname{grSQCycle} + \item \tkzcname{grWheel} + \item \tkzcname{grLadder} + \item \tkzcname{grPrism} + \item \tkzcname{grCompleteBipartite} + \item \tkzcname{grTriangularGrid} + \item \tkzcname{grLCF} + \item \tkzcname{grWriteExplicitLabels} + \item \tkzcname{grWriteExplicitLabel} + \item \tkzcname{AssignVertexLabel} + \end{itemize} +\end{multicols} + +Classic graphs : + +\medskip + +\begin{multicols}{2} + \begin{itemize} +\item \tkzcname{grAndrasfai} +\item \tkzcname{grBalaban} +\item \tkzcname{grChvatal} +\item \tkzcname{grCocktailParty} +\item \tkzcname{grCrown} +\item \tkzcname{grCubicalGraph} +\item \tkzcname{grDesargues} +\item \tkzcname{grDodecahedral} +\item \tkzcname{grDoyle} +\item \tkzcname{grFoster} +\item \tkzcname{grFolkman} +\item \tkzcname{grFranklin} +\item \tkzcname{grGeneralizedPetersen} +\item \tkzcname{grGrotzsch} +\item \tkzcname{grHeawood} +\item \tkzcname{grIcosahedral} +\item \tkzcname{grKonisberg} +\item \tkzcname{grLevi} +\item \tkzcname{grMcGee} +\item \tkzcname{grMobiusKantor} +\item \tkzcname{grMobiusLadder} +\item \tkzcname{grOctahedral} +\item \tkzcname{grPappus} +\item \tkzcname{grPetersen} +\item \tkzcname{grRobertson} +\item \tkzcname{grRobertsonWegner} +\item \tkzcname{grTetrahedral} +\item \tkzcname{grTutteCoxeter} +\item \tkzcname{grWong} +\end{itemize} +\end{multicols} + + +See the document "NamedGraph" for all the classic named graphs that you can draw with the package \tkzname{tkz-berge.sty}. +\include{TKZdoc-berge-macros} +\include{TKZdoc-berge-macros-e} +\include{TKZdoc-berge-classic} +\include{TKZdoc-berge-style} + +\clearpage\newpage +\small\printindex + +\end{document} + + + +
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-style.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-style.tex new file mode 100644 index 00000000000..cfb0934e1ca --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-berge-style.tex @@ -0,0 +1,58 @@ +\section{Macros and Styles} + +\subsection{How to change the background color and text color} + +You can use the following macro : + +\begin{NewMacroBox}{tkzSetUpColors}{\oarg{local options}} + +\begin{tabular}{llc} + Options & default & definition \\ +\midrule +\TOline{background} {white} {couleur du fond } +\TOline{text} {black} {couleur du texte } +\end{tabular} +\end{NewMacroBox} + + + + +\subsection{Modification of labels \tkzcname{AssignVertexLabel}} + +\begin{NewMacroBox}{AssignVertexLabel}{\oarg{local options}\var{prefix}\var{List of names}} +\begin{tabular}{lll} + Arguments & & example \\ +\midrule +\TAline{prefix} {} {\tkzcname{AssignVertexLabel\{a\}\{Alter\}}} +\TAline{List of names} {} {\tkzcname{AssignVertexLabel\{a\}\{Paris,Lyon\}}} +\bottomrule +\end{tabular} + +\medskip +\begin{tabular}{llc} + Options & default & definition \\ +\midrule +\TOline{size} {\tkzcname{normalsize}} {taille de la fonte } +\TOline{color} {black} {couleur du texte } +\TOline{Math} {false} {math mode } +\end{tabular} +\end{NewMacroBox} + +\medskip +\subsubsection{AssignStyle and \tkzcname{AssignVertexLabel}} +First step : We create an empty graph without labels. + +Second step : We place labels with the macro \tkzcname{AssignVertexLabel} \begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \SetVertexNoLabel + \grCycle{6} + \tikzset{AssignStyle/.append style = {below=12pt}} + \AssignVertexLabel[color = blue,% + size = \footnotesize]{a}{% + Paris,Lyon,Marseille,Bordeaux,Reims,Saint-Etienne} +\end{tikzpicture} +\end{tkzexample} +\end{center} + +\endinput
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-gr-installation.tex b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-gr-installation.tex new file mode 100644 index 00000000000..93224a0f42c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/doc/latex/TKZdoc-gr-installation.tex @@ -0,0 +1,91 @@ +\chap{Installation}\label{ins} + +You could simply create a folder (directory) \tikz[remember picture,baseline=(n1.base)]\node [fill=green!50,draw] (n1) {prof}; which path is : \colorbox{red!50}{ texmf/tex/latex/prof}. \colorbox{green!50}{texmf} is generally the personnal folder, here ways of this folder on my two computers: + +\medskip +\begin{itemize}\setlength{\itemsep}{10pt} +\item with OS X \colorbox{blue!30}{\textbf{/Users/ego/Library/texmf}}; +\item with Ubuntu \colorbox{blue!30}{\textbf{/home/ego/texmf}}. +\end{itemize} + +If you choose a custom location for your files, I suppose that you know why! +The installation that I propose, is valid only for one user. + +\medskip +\begin{enumerate} +\item Store the files \tikz[remember picture,baseline=(n2.base)]\node [fill=green!50,draw] (n2) {tkz-arith.sty, tkz-graph.sty and tkz-berge.sty}; in the folder \colorbox{green!50}{prof}. +\item Open a terminal, then type \colorbox{red!50}{|sudo texhash|} + +\medskip +\begin{figure}[htbp] + \begin{center} + \includegraphics[scale=.5]{term.pdf} + \end{center} +\end{figure} + +\item Check that \textcolor{red}{xkeyval, ifthen and tikz 2.0} are installed because they are obligatory. +\end{enumerate} + +My folder texmf is structured as in the diagram below: + +\medskip +\begin{tikzpicture} [remember picture,rotate=90] + +\node (texmf) at (4,2) [draw,fill=blue!30 ] {texmf}; +\node (tex) at (6,0) [draw ] {tex}; +\node (doc) at (0,0) [draw ] {doc}; +\node (generic) at (7,-4) [draw ] {generic}; +\node (docgen) at (0,-4) [draw ] {generic}; +\node (latex) at (4,-4) [draw ] {latex}; +\node (pgf) at (7,-7) [draw,fill=orange] {pgf}; +\node (pre) at (6,-7) [draw,fill=orange] {pgf}; +\node (xkey) at (5,-7) [draw ] {xkeyval}; +\node (four) at (4,-7) [draw ] {fourier}; +\node (prof) at (3,-7) [draw,fill=green ] {{prof}}; +\node (etc) at (2,-7) [draw ] {etc...}; +\node (dpgf) at (0,-7) [draw,fill=orange] {pgf}; +\node (cls) at (8,-11) [draw,fill=green ] {prof.cls}; +\node (qcm) at (7,-11) [draw,fill=green ] {alterqcm.sty}; +\node (fonc) at (6,-11) [draw,fill=orange] {tkz-base.sty}; +\node (esp) at (5,-11) [draw,fill=orange] {tkz-fct.sty}; +\node (tuk) at (4,-11) [draw,fill=orange] {tkz-arith.sty}; +\node (tab) at (3,-11) [draw,fill=orange] {tkz-2d.sty}; +\node (base) at (2,-11) [draw,fill=orange] {tkz-tab.sty}; +\node (gra) at (1,-11) [draw,fill=orange] {tkz-berge.sty}; +\node (pcfg) at (0,-11) [draw,fill=green ] {prof.cfg}; +\node (ppcfg) at (-1,-11) [draw,fill=green ] {profparam.cfg}; +\node (bbp) at (-2,-11) [draw,fill=orange] {bbpage.cfg}; +\draw (doc.west) |- (4, 1); +\draw (tex.west) |- (4, 1); +\draw (latex.west) |- (6,-2); +\draw (generic.west) |- (6,-2); +\draw (xkey.west) |- (5,-6); +\draw (prof.west) |- (3,-6); +\draw (four.west) |- (4,-6); +\draw (pre.west) |- (4,-6); +\draw (etc.west) |- (4,-6); +\draw (cls.west) |- (4,-9); +\draw (qcm.west) |- (7,-9); +\draw (fonc.west) |- (6,-9); +\draw (esp.west) |- (5,-9); +\draw (tuk.west) |- (4,-9); +\draw (tab.west) |- (3,-9); +\draw (base.west) |- (2,-9); +\draw (gra.west) |- (1,-9); +\draw (pcfg.west) |- (0,-9); +\draw (ppcfg.west) |- (-1,-9); +\draw (bbp.west) |- (4,-9); +\draw[-open triangle 90] (pgf.west) -- (generic.east); +\draw[-open triangle 90] (4,1) -- (texmf.east); +\draw[-open triangle 90] (6,-2) -- (tex.east); +\draw[-open triangle 90] (4,-6) -- (latex.east); +\draw[-open triangle 90] (3,-9) -- (prof.east); +\draw[-open triangle 90] (dpgf.west) -- (docgen.east); +\draw[-open triangle 90] (docgen.west) -- (doc.east); +\end{tikzpicture} + +\begin{tikzpicture}[remember picture,overlay] + \path[->,thin,red,>=latex] (n1) edge [bend left] (prof); + \path[->,thin,red,>=latex] (n2) edge [bend left] (prof); +\end{tikzpicture} +\endinput
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+\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +%\usetikzlibrary{calc} +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{blue!60!black!30}{blue}{white} +\begin{center} + \begin{tikzpicture} + \grGrid[Math,RA=2,RB=2]{3}{5} + \end{tikzpicture} +\end{center} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Circulant.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Circulant.tex new file mode 100644 index 00000000000..678de92ceaa --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Circulant.tex @@ -0,0 +1,51 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} + +\begin{document} + + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3.5]{4}{1} +\end{tikzpicture} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3.5]{6}{1,3} +\end{tikzpicture} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3.5]{8}{1,3} +\end{tikzpicture} +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3.5]{10}{1,3,5} +\end{tikzpicture} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] + \grCirculant[RA=3.5]{12}{1,3,5} +\end{tikzpicture} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3.5]{14}{1,3,5,7} +\end{tikzpicture} + +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3.5]{16}{1,3,5,7} +\end{tikzpicture} +\begin{tikzpicture} + \GraphInit[vstyle=Art] +\grCirculant[RA=3.5]{21}{1} +\end{tikzpicture} +% +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Complet-16.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Complet-16.tex new file mode 100644 index 00000000000..e7563b31a51 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-Complet-16.tex @@ -0,0 +1,28 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} + +\begin{document} + +\begin{center} +\begin{tikzpicture} + \SetVertexNoLabel + \tikzstyle{VertexStyle}=[shape = circle, + shading = ball, + ball color = green!40!black,% + minimum size = 20pt,% + draw] + \tikzstyle{EdgeStyle} =[thick,% + double= orange,% + double distance = 1pt] + \grCirculant[RA=6]{16}{2,3,4,5,6,7,8} +\end{tikzpicture} +\end{center} +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-edgeingraphmodloop.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-edgeingraphmodloop.tex new file mode 100644 index 00000000000..86df8303428 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/gr-edgeingraphmodloop.tex @@ -0,0 +1,26 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +\begin{document} + \begin{tikzpicture} + \grEmptyCycle[RA=4]{7} + \EdgeInGraphModLoop{a}{7}{2}{1} + \end{tikzpicture} + + \begin{tikzpicture} + \grEmptyCycle[RA=4]{8} + \EdgeInGraphModLoop{a}{8}{2}{1} + \end{tikzpicture} + + \begin{tikzpicture} + \grEmptyCycle[RA=4]{8} + \EdgeInGraphModLoop{a}{8}{3}{1} + \end{tikzpicture} +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grCLadder.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grCLadder.tex new file mode 100644 index 00000000000..626f3e7cec3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grCLadder.tex @@ -0,0 +1,39 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} + +\begin{document} + +\tikzstyle{EdgeStyle}= [thick,% + double = orange,% + double distance = 1pt] +\begin{center} + + \tikzstyle{VertexStyle}=[shape = circle, + shading = ball, + ball color = green!30, + minimum size = 24pt, + draw] + \SetVertexLabel + \tikzstyle{EdgeStyle}= [color=red!30, + double= green!50!black, + double distance = 2pt] +\begin{tikzpicture} +\grPrism[RA=5,RB=3]{6}% +\end{tikzpicture} + +\begin{tikzpicture} +\grPrism[RA=5,RB=3]{4}% +\end{tikzpicture} + + +\end{center} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grDoubleMod.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grDoubleMod.tex new file mode 100644 index 00000000000..42c2fccbd4b --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grDoubleMod.tex @@ -0,0 +1,23 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +%\usetikzlibrary{calc} +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{blue!60!black!30}{blue}{white} +\begin{center} + \begin{tikzpicture} + \grCycle[RA=7]{27} + \EdgeDoubleMod{a}{27}{0}{3} + {a}{27}{13}{3}{9} + \end{tikzpicture} +\end{center} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grExtraChords.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grExtraChords.tex new file mode 100644 index 00000000000..c3ce1095fe1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grExtraChords.tex @@ -0,0 +1,64 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} + +\begin{document} + +\tikzstyle{VertexStyle}=[shape = circle,% + fill = red!50, + very thin, + inner sep = 0pt,% + minimum size = 16pt, + draw] +\tikzstyle{EdgeStyle}= [thick,% + double= lightgray,% + double distance = 1pt] + + \SetVertexLabel +\begin{tikzpicture} + \grEmptyCycle[RA=4]{30} + \EdgeInGraphMod*{a}{30}{9}{1}{6} +\end{tikzpicture} + +\begin{tikzpicture} + \grEmptyCycle[RA=4]{30} + \EdgeInGraphMod{a}{30}{9} +\end{tikzpicture} + +\begin{tikzpicture} + \grEmptyCycle[RA=5]{30} + \EdgeInGraphMod*{a}{30}{9}{1}{6} +\end{tikzpicture} + +\begin{center} + \begin{tikzpicture}[rotate=90] + \grLCF[RA=6]{6,12}{15} + \end{tikzpicture} +\end{center} + + +\begin{center} + \begin{tikzpicture}[rotate=90] + \grLCF[RA=6]{6,12}{15} + \SetUpEdge[color=red] + \EdgeInGraphMod*{a}{30}{9}{1}{6} + \end{tikzpicture} +\end{center} + +\begin{center} + \begin{tikzpicture}[rotate=90] + \grLCF[RA=6]{6,12}{15} + \EdgeInGraphMod*{a}{30}{9}{1}{6} + \EdgeInGraphMod*{a}{30}{15}{2}{6} + \EdgeInGraphMod*{a}{30}{9}{3}{6} + \end{tikzpicture} +\end{center} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grLadder.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grLadder.tex new file mode 100644 index 00000000000..d2ab402846d --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grLadder.tex @@ -0,0 +1,27 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +%\usetikzlibrary{calc} +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{green!30}{green!50!black}{red!30} +\begin{center} +\begin{tikzpicture} +\grLadder[RA=2,RS=3]{6}% +\end{tikzpicture} +\end{center} + +\begin{center} +\begin{tikzpicture} +\grLadder[RA=3,RS=4]{4}% +\end{tikzpicture} +\end{center} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grSQCycle.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grSQCycle.tex new file mode 100644 index 00000000000..fade3b4f646 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grSQCycle.tex @@ -0,0 +1,34 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +%\usetikzlibrary{calc} +\thispagestyle{empty} +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{black!50}{darkgray}{white} + \SetVertexMath +\begin{center} + \begin{tikzpicture} + \grSQCycle[RA=5]{8}% + \end{tikzpicture} +\end{center} + +\begin{center} + \begin{tikzpicture} + \grSQCycle[RA=5]{6}% + \end{tikzpicture} +\end{center} + +\begin{center} + \begin{tikzpicture} + \grSQCycle[RA=5]{9}% + \end{tikzpicture} +\end{center} +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grStar.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grStar.tex new file mode 100644 index 00000000000..4a0d75d9191 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grStar.tex @@ -0,0 +1,37 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} + +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{orange!60}{red}{white} + \SetVertexMath +\begin{center} + \begin{tikzpicture} + \grEmptyStar[RA=3]{6} + \end{tikzpicture} +\end{center} + + +\begin{center} + \begin{tikzpicture} + \grStar[RA=3]{7} + \end{tikzpicture} +\end{center} + + +\begin{center} + \begin{tikzpicture} + \grStar[RA=4]{10} + \end{tikzpicture} +\end{center} + + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grWheel.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grWheel.tex new file mode 100644 index 00000000000..28f563de4c0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/grWheel.tex @@ -0,0 +1,28 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +\begin{document} + \GraphInit[vstyle=Shade] + \SetGraphShadeColor{orange!60!black!30}{Brown}{white} +\begin{center} + \begin{tikzpicture} + \grWheel[RA=3]{5} + \end{tikzpicture} +\end{center} + + +\begin{center} + \begin{tikzpicture} + \grWheel[RA=4]{10} + \end{tikzpicture} +\end{center} + + +\end{document} diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercube_simple.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercube_simple.tex new file mode 100644 index 00000000000..8ae56a4875c --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercube_simple.tex @@ -0,0 +1,32 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +\begin{document} +\SetVertexSimple +\SetVertexNoLabel +\begin{center} + \begin{tikzpicture} + \grCycle[RA=8]{8} + \pgfmathparse{8*(1-4*sin(22.5)*sin(22.5))} + \let\tkzbradius\pgfmathresult + \grCirculant[prefix=b,RA=\tkzbradius]{8}{3} +\makeatletter + \foreach \vx in {0,...,7}{% + \pgfmathsetcounter{tkz@gr@n}{mod(\vx+1,8)} + \pgfmathsetcounter{tkz@gr@a}{mod(\vx+7,8)} + \pgfmathsetcounter{tkz@gr@b}{mod(\thetkz@gr@n+1,8)} + \Edge(a\thetkz@gr@n)(b\thetkz@gr@b) + \Edge(b\thetkz@gr@a)(a\vx) + } +\makeatother +\end{tikzpicture} +\end{center} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercubed.tex b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercubed.tex new file mode 100644 index 00000000000..f5c33f46931 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tkz-berge/examples/latex/hypercubed.tex @@ -0,0 +1,38 @@ +% Author : Alain Matthes +% Encoding : UTF8 +% Engine : PDFLaTeX +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[usenames,dvipsnames]{xcolor} +\usepackage{fullpage} +\usepackage[upright]{fourier} +\usepackage{tkz-berge} +\thispagestyle{empty} +\begin{document} +\tikzstyle{SimpleVertexStyle} = [shape = circle,% + fill = red,% + inner sep = 3pt,% + outer sep = 0pt,% + draw] +\SetVertexSimple +\SetVertexNoLabel + +\begin{center} + \begin{tikzpicture} + \grCycle[RA=8]{8} + \pgfmathparse{8*(1-4*sin(22.5)*sin(22.5))} + \let\tkzbradius\pgfmathresult + \grCirculant[prefix=b,RA=\tkzbradius]{8}{3} + \makeatletter + \foreach \vx in {0,...,7}{% + \pgfmathsetcounter{tkz@gr@n}{mod(\vx+1,8)} + \pgfmathsetcounter{tkz@gr@a}{mod(\vx+7,8)} + \pgfmathsetcounter{tkz@gr@b}{mod(\thetkz@gr@n+1,8)} + \Edge(a\thetkz@gr@n)(b\thetkz@gr@b) + \Edge(b\thetkz@gr@a)(a\vx) + }\makeatother + \end{tikzpicture} + +\end{center} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/tex/latex/tkz-berge/tkz-berge.sty b/Master/texmf-dist/tex/latex/tkz-berge/tkz-berge.sty new file mode 100644 index 00000000000..be735bc3d88 --- /dev/null +++ b/Master/texmf-dist/tex/latex/tkz-berge/tkz-berge.sty @@ -0,0 +1,1838 @@ + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % % + % tkz-berge.sty encodage : utf8 % + % % + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % % + % Créé par Alain Matthes le 08-05-2007. % + % contribution : Rafael Villarroel 2007 (RV) % + % contribution : Rafael Villarroel 2009 (RV) % + % % + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + % modif Doyle form 1 + % add \setkeys[GR]{edge}{#1}% in edge's macros + % remove somme bugs with pgf 2.00 cvs + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%% Objet : Création de graphes classiques +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{tkz-berge}[2011/06/01 2.00 tkz-berge for named graphs] + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\RequirePackage{tkz-graph} +\def\tkzutil@empty{} +\def\tkzutil@firstofone#1{#1} +\def\tkzutil@firstoftwo#1#2{#1} +\def\tkzutil@secondoftwo#1#2{#2} +%<--------------------------------------------------------------------------–> +\long\def\tkzutil@ifundefined#1{% + \expandafter\ifx\csname#1\endcsname\relax + \expandafter\tkzutil@firstoftwo + \else + \expandafter\tkzutil@secondoftwo + \fi} +%\input{tkz-tools-arith.tex} +\tkzutil@ifundefined{pgfmath@function@isfactor}{% + \pgfmathdeclarefunction{isfactor}{2}{% +\begingroup +\c@pgfmath@counta#1\relax% +\c@pgfmath@countb#2\relax% +\c@pgfmath@countc#1\relax% +\divide\c@pgfmath@counta by\c@pgfmath@countb% +\multiply\c@pgfmath@counta by\c@pgfmath@countb% +\advance\c@pgfmath@countc by-\c@pgfmath@counta% +\ifnum\c@pgfmath@countc=0 \def\pgfmathresult{1}% +\else + \def\pgfmathresult{0}% + \fi +\pgfmath@smuggleone\pgfmathresult% +\endgroup} +}{} + + +\edef\tkzAtCode{\the\catcode`\@} +\catcode`\@=11\relax +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcounter{tkz@bg@cnt} +% NAMED GRAPHS +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Graphes cls +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\define@cmdkey [GR] {cl} {L}{} +\define@boolkey [GR] {cl} {Math}[true]{} +\define@boolkey [GR] {cl} {inv}[true]{} +\define@cmdkey [GR] {cl} {RA}{} +\define@cmdkey [GR] {cl} {RB}{} +\define@cmdkey [GR] {cl} {RC}{} +\define@cmdkey [GR] {cl} {RD}{} +\define@cmdkey [GR] {cl} {RE}{} +\define@cmdkey [GR] {cl} {RS}{} +\define@cmdkey [GR] {cl} {prefix}{} +\define@cmdkey [GR] {cl} {prefixx}{} +\define@cmdkey [GR] {cl} {prefixxx}{} +\define@cmdkey [GR] {cl} {prefixxxx}{} +\define@cmdkey [GR] {cl} {prefixxxxx}{} +\define@cmdkey [GR] {cl} {form}{} +\define@cmdkey [GR] {cl} {num}{} +\define@cmdkey [GR] {cl} {rotation}{} +\define@cmdkey [GR] {cl} {x}{} +\define@cmdkey [GR] {cl} {y}{} +\define@cmdkey [GR] {cl} {r}{} +\define@cmdkey [GR] {cl} {d}{} +\presetkeys [GR] {cl} {RA = 4, + RB = 3, + RC = 2, + RD = 1, + RE = 0.5, + RS = 0, + form = 1, + prefix = a, + prefixx = b, + prefixxx = c, + prefixxxx = d, + prefixxxxx = e, + num = {}, + Math = false, + x = 0, + y = 0, + r = 0, + d = 0, + rotation = 0}{} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Tools Graphes particuliers +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Some tools +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grMathSep}{_} +\newcommand*{\grLabelSep}{;} + +\newcommand*{\write@math}[3]{% + \Vertex[x = #1,y = #2,% + L = \cmdGR@cl@prefix\grMathSep{#3}]{\cmdGR@cl@prefix#3}} +\newcommand*{\write@nomath}[3]{% + \Vertex[x = #1,y = #2]{\cmdGR@cl@prefix#3}} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Empty graphs +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grEmptyCycle}{\@ifstar% + \grEmptyCycleStar% + \grEmptyCycleNoStar} +\newcommand*{\grEmptyCycleNoStar}[2][]{% + \begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \edef\tkz@auxctp{\thetkz@gr@p} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathparse{360/#2*\V@x+\cmdGR@cl@rotation} + \let\tkz@angle\pgfmathresult% +\pgfmathsetmacro{\x@result}{% + \cmdGR@cl@RA*cos(\tkz@angle)+\cmdGR@cl@r*cos(\cmdGR@cl@d)} + \pgfmathsetmacro{\y@result}{% + \cmdGR@cl@RA*sin(\tkz@angle)+\cmdGR@cl@r*sin(\cmdGR@cl@d)} + \ifGR@cl@Math% + \presetkeys [GR] {vertex} {Math = true}{}% + \Vertex[x = \x@result+\cmdGR@cl@x,% + y = \y@result+\cmdGR@cl@y,% + L = \cmdGR@cl@prefix\grMathSep{\V@x}]{\cmdGR@cl@prefix\V@x}% + \else% + \Vertex[x = \x@result+\cmdGR@cl@x,% + y = \y@result+\cmdGR@cl@y]{\cmdGR@cl@prefix\V@x}% + \fi% + }% + \endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand{\grEmptyCycleStar}[2][]{% + \begingroup% + \setkeys[GR]{cl}{#1}% + \setcounter{tkz@gr@a}{0} + \setcounter{tkz@gr@b}{0} + \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}} + \foreach \V@x in {#2}{% + \pgfmathsetmacro{\x@result}{% + \cmdGR@cl@RA*cos((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)% + +\cmdGR@cl@r*cos(\cmdGR@cl@d)% + } + \pgfmathsetmacro{\y@result}{% + \cmdGR@cl@RA*sin((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)% + +\cmdGR@cl@r*sin(\cmdGR@cl@d)% + } + \ifGR@cl@Math% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}% + \else% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}% + \fi% + \stepcounter{tkz@gr@a}% + } + \endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grEmptyPath from (RV) +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grEmptyPath}{\@ifstar% + \grEmptyPathStar% + \grEmptyPathNoStar} +\newcommand*{\grEmptyPathNoStar}[2][]{% +\begingroup% +\setkeys[GR]{cl}{#1}% +\pgfmathsetcounter{tkz@gr@a}{#2-1} +\edef\tkz@auxctp{\thetkz@gr@a} + \ifcase\cmdGR@cl@form +\or +\def\tkzb@result{0} +\foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(\V@x)*cos(\cmdGR@cl@rotation)} + \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(\V@x)*sin(\cmdGR@cl@rotation)} + \pgfmathsetmacro{\x@coord}{\x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)} + \pgfmathsetmacro{\y@coord}{\y@result+\cmdGR@cl@y+ + \cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS} + \ifGR@cl@Math% + \presetkeys [GR] {vertex} {Math = true}{}% + \ifthenelse{\equal{\cmdGR@cl@num}{}}{% + \write@math{\x@coord}{\y@coord}{\V@x}}{% + \write@math{\x@coord}{\y@coord}{\V@x\grLabelSep\cmdGR@cl@num}}% + \else + \ifthenelse{\equal{\cmdGR@cl@num}{}}{% + \write@nomath{\x@coord}{\y@coord}{\V@x}}{% + \write@nomath{\x@coord+\cmdGR@cl@x}{\y@coord}{% + \V@x\grLabelSep\cmdGR@cl@num}}% + \fi}% + \or +\foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetmacro{\x@result}{% + \cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*cos(\cmdGR@cl@rotation)} + \pgfmathsetmacro{\y@result}{% + \cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*sin(\cmdGR@cl@rotation)} + \pgfmathsetmacro{\x@coord}{% + \x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)} + \pgfmathsetmacro{\y@coord}{% + \y@result+\cmdGR@cl@y+\cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS} + \ifGR@cl@Math% + \presetkeys [GR] {vertex} {Math = true}{}% + \ifthenelse{\equal{\cmdGR@cl@num}{}}{% + \write@math{\x@coord}{\y@coord}{\V@x}}{% + \write@math{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}% + \else + \ifthenelse{\equal{\cmdGR@cl@num}{}}{% + \write@nomath{\x@coord}{\y@coord}{\V@x}}{% + \write@nomath{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}% + \fi +}% +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand{\grEmptyPathStar}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \setcounter{tkz@gr@a}{0} + \ifcase\cmdGR@cl@form + \or + % form 1 + \foreach \V@x in {#2}{% + \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*cos(\cmdGR@cl@rotation)% + +\cmdGR@cl@r*cos(\cmdGR@cl@d)}% + \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*sin(\cmdGR@cl@rotation)% + +\cmdGR@cl@r*sin(\cmdGR@cl@d)}% + \ifGR@cl@Math% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}% + \else% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}% + \fi% + \stepcounter{tkz@gr@a}% + }% + \or + % form 2 + \setcounter{tkz@gr@a}{0} + \setcounter{tkz@gr@b}{0} + \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}} + \foreach \V@x in {#2}{% + \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5% + *cos(\cmdGR@cl@rotation)% + +\cmdGR@cl@r*cos(\cmdGR@cl@d)% + } + \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5% + *sin(\cmdGR@cl@rotation)% + +\cmdGR@cl@r*sin(\cmdGR@cl@d)% + } + \ifGR@cl@Math% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}% + \else% + \Vertex[% + x=\x@result+\cmdGR@cl@x, + y=\y@result+\cmdGR@cl@y, + L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}% + \fi% + \stepcounter{tkz@gr@a} + } + \fi + \endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grEmptyStar +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grEmptyStar}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}% + \write@math{0}{0}{\thetkz@gr@a}% + \else + \write@nomath{0}{0}{\thetkz@gr@a}% + \fi + \grEmptyCycle[#1]{\thetkz@gr@a} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grEmptyGrid +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand{\grEmptyGrid}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \edef\tkz@auxctpa{\thetkz@gr@a} + \pgfmathsetcounter{tkz@gr@b}{#3-1} + \edef\tkz@auxctpb{\thetkz@gr@b} + \foreach \V@x in {0,...,\tkz@auxctpa}{% + \foreach \V@y in {0,...,\tkz@auxctpb}{% + \ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}% + \write@math{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}% + \else + \write@nomath{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}% + \fi}% + } +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grEmptyLadder +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grEmptyLadder}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grEmptyPath[#1,RS=0]{#2} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grEmptyPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2} +\endgroup% +} + + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Edges +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeInGraphFromOneToComp}[4][]{% #4 +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@ta}{#3-1} + \edef\tkz@auxctp{\thetkz@gr@ta} + \foreach \cx in {0,...,\tkz@auxctp}{% + \ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#2\cx)}% + }% +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% new tool EdgeInGraphLoop loop 0--1--2.........n--0 +% star 0--1--2.........n- +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeInGraphLoop}{\@ifstar% + \EdgeInGraphLoopStar% + \EdgeInGraphLoopNoStar} +\newcommand*{\EdgeInGraphLoopNoStar}[3][]{% #4 +\begingroup% +\setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@ta}{#3-1} + \setcounter{tkz@gr@n}{0} + \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n) + \pgfmathaddtocounter{tkz@gr@ta}{-1} + \edef\tkz@auxctp{\thetkz@gr@ta} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \stepcounter{tkz@gr@n} + \Edge[#1](#2\V@x)(#2\thetkz@gr@n)% + }% +\endgroup% +} +\newcommand*{\EdgeInGraphLoopStar}[3][]{% #4 +\begingroup% +\setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@ta}{#3-2} + \setcounter{tkz@gr@n}{0} + \edef\tkz@auxctp{\thetkz@gr@ta} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \stepcounter{tkz@gr@n} + \Edge[#1](#2\V@x)(#2\thetkz@gr@n)% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% new tool EdgeInGraphMod replace nextmod +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeInGraphMod}{\@ifstar% + \EdgeInGraphModStar% + \EdgeInGraphModNoStar} +\newcommand*{\EdgeInGraphModNoStar}[4][]{% #2 order +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@ta}{#3-1} + \edef\tkz@auxctp{\thetkz@gr@ta} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#4,#3)} + \Edge[#1](#2\thetkz@gr@tb)(#2\V@x)% + }% +\endgroup% +} +%#1 prefix #2 order #3 add #4 start #5 décalage +\newcommand*{\EdgeInGraphModStar}[6][]{% +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@ta}{#5} + \whiledo{\value{tkz@gr@ta}<#3}{% + \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)} + \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n) + \pgfmathaddtocounter{tkz@gr@ta}{#6}% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeInGraphModLoop dep #4 add #3 mod #2 until #4 +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand*{\EdgeInGraphModLoop}[5][]{% #2 order +\begingroup% + \setkeys[GR]{edge}{#1}% + \setcounter{tkz@gr@ta}{#5} + \setcounter{tkz@gr@n}{#3} + \whiledo{\not\equal{\value{tkz@gr@n}}{#5}}{% + \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)} + \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)% + \setcounter{tkz@gr@ta}{\thetkz@gr@n} + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeIdentity +% la version étoilée permet d'utliser une sélection +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeIdentity}{\@ifstar% + \EdgeIdentityStar% + \EdgeIdentityNoStar} +\newcommand*{\EdgeIdentityNoStar}[4][]{% +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@e}{#4-1} + \edef\tkz@auxctp{\thetkz@gr@e} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \Edge[#1](#2\V@x)(#3\V@x)% + }% +\endgroup% +} +\newcommand*{\EdgeIdentityStar}[4][]{% +\begingroup% + \setkeys[GR]{edge}{#1}% + \foreach \V@x in {#4}{% + \Edge[#1](#2\V@x)(#3\V@x)% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeFromOneToAll vertex #1#3 through #2 0...#2 n-1 #5 order of the graph +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeFromOneToAll}[5][]{% #4 = order of the graph +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@e}{#5-1} + \edef\tkz@auxctp{\thetkz@gr@e} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \Edge[#1](#2#4)(#3\V@x)% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeFromOneToSeq vertex #1#3 through #2#4...#2#5 +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeFromOneToSeq}[6][]{% #4 +\begingroup% + \setkeys[GR]{edge}{#1}% + \foreach \V@x in {#5,...,#6}{% + \Edge[#1](#2#4)(#3\V@x)% + }% +\endgroup% +} %<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeFromOneToSel vertex #1#3 through #2#4...#2#5 +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeFromOneToSel}[5][]{% #4 +\begingroup% + \setkeys[GR]{edge}{#1}% + \foreach \V@x in {#5}{% + \Edge[#1](#2#4)(#3\V@x)% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeFromOneToComplement vertex #1#3 through #2#4...#2#5 +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeFromOneToComp}[5][]{% +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@e}{#5-1} + \edef\tkz@auxctp{\thetkz@gr@e} + \foreach \cx in {0,...,\tkz@auxctp}{% + \ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#3\cx)}% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% new tool EdgeMod replace nextmod +% identity with step like nextmod ??? +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeMod}{\@ifstar% + \EdgeModStar% + \EdgeModNoStar} +\newcommand*{\EdgeModNoStar}[5][]{%#3 order #4 step +\begingroup% + \setkeys[GR]{edge}{#1}% + \pgfmathsetcounter{tkz@gr@e}{#4-1} + \edef\tkz@auxctp{\thetkz@gr@e} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#5,#4)} + \Edge[#1](#2\V@x)(#3\thetkz@gr@tb)% + }% +\endgroup% +} +%#1 prefix #2 prefix #3 order #4 order inf #5 step +\newcommand*{\EdgeModStar}[6][]{% +\begingroup% + \setkeys[GR]{edge}{#1}% + \setcounter{tkz@gr@ta}{0} + \whiledo{\value{tkz@gr@ta}<#4}{% + \pgfmathsetcounter{tkz@gr@tb}{Mod(\thetkz@gr@ta+#5,#4)} + \Edge[#1](#2\thetkz@gr@ta)(#3\thetkz@gr@tb)% + \pgfmathaddtocounter{tkz@gr@ta}{#6}}% +\endgroup% +}% +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% new tool EdgeInGraphSeq sequence i--i+1--.....--j +% or i--i+k--...--j +% #1 options #2 graph #3 from #4 to +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeInGraphSeq}[4][]{% #4 +\begingroup% +\setkeys[GR]{edge}{#1}% + \foreach \V@x in {#3,...,#4}{% + \pgfmathsetcounter{tkz@gr@n}{\V@x+1} + \Edge[#1](#2\V@x)(#2\thetkz@gr@n)}% +\endgroup% +}% + +%%%%%%%%%%% NEW COMMANDS +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% new tool EdgeSeq sequence +% #1 options #2 first graph #3 second graph #4 from #5 to +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand{\EdgeSequence}[5][]{% +\begingroup% +\setkeys[GR]{edge}{#1}% + \foreach \V@x in {#4,...,#5}{% + \pgfmathsetcounter{tkz@gr@n}{\V@x+1} + \Edge[#1](#2\V@x)(#3\thetkz@gr@n)}% +\endgroup% +}% +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% EdgeDoubleMod by RV +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\EdgeDoubleMod}[9]{% +\begingroup% + \foreach \V@x in {0,...,#9}{% + \pgfmathsetcounter{tkz@gr@c}{Mod(#3+(#4*\V@x),#2)} + \pgfmathsetcounter{tkz@gr@n}{Mod(#7+(#8*\V@x),#6)} + \Edge(#1\thetkz@gr@c)(#5\thetkz@gr@n) + }% +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPath +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grPath}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grEmptyPath[#1]{#2} + \ifthenelse{\equal{\cmdGR@cl@num}{}}{% + \ifthenelse{\equal{#2}{1}}{}{% + \EdgeInGraphLoop*{\cmdGR@cl@prefix}{#2}% + }}{% + \ifthenelse{\equal{#2}{1}}{}{% + \ifcase\cmdGR@cl@form + \or + \pgfmathsetcounter{tkz@gr@ta}{#2-2} + \setcounter{tkz@gr@n}{0} + \edef\tkz@auxctp{\thetkz@gr@ta} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \stepcounter{tkz@gr@n} + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\cmdGR@cl@num)% + (\cmdGR@cl@prefix\thetkz@gr@n\grLabelSep\cmdGR@cl@num)% + }% + \or + \EdgeInGraphLoop*{\cmdGR@cl@prefix\cmdGR@cl@num\grLabelSep}{#2} + \fi% + }} +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grGrid +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grGrid}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grEmptyGrid[#1]{#2}{#3} + \pgfmathsetcounter{tkz@gr@a}{#2-2} + \edef\tkz@auxctpa{\thetkz@gr@a} + \pgfmathsetcounter{tkz@gr@b}{#3-2} + \edef\tkz@auxctpb{\thetkz@gr@b} + \foreach \V@x in {0,...,\tkz@auxctpa}{% + \foreach \V@y in {0,...,\tkz@auxctpb}{% + \pgfmathsetcounter{tkz@gr@c}{\V@x+1} + \pgfmathsetcounter{tkz@gr@d}{\V@y+1} + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)% + (\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@d) + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)% + (\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\V@y)% + }% + }% + \pgfmathsetcounter{tkz@gr@a}{#2-2} + \pgfmathsetcounter{tkz@gr@b}{#3-1} + \edef\tkz@auxctpa{\thetkz@gr@a} + \foreach \V@x in {0,...,\tkz@auxctpa}{% + \pgfmathsetcounter{tkz@gr@c}{\V@x+1} + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)% + (\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\thetkz@gr@b)% + }% + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \pgfmathsetcounter{tkz@gr@b}{#3-2} + \edef\tkz@auxctpb{\thetkz@gr@b} + \foreach \V@y in {0,...,\tkz@auxctpb}{% + \pgfmathsetcounter{tkz@gr@d}{\V@y+1} + \Edge(\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\V@y)% + (\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\thetkz@gr@d)% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grComplete +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grComplete}[2][]{% #1 options #2 ordre du graphe +\begingroup% + \setkeys[GR]{cl}{#1}% + \grEmptyCycle[#1]{#2}% + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \ia in {0,...,\tkz@auxctp}% + {\foreach \ib in {\ia,...,\tkz@auxctp} + {\Edge(\cmdGR@cl@prefix\ia)(\cmdGR@cl@prefix\ib)}% + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCycle +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCycle}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1} + \grEmptyCycle[#1]{#2} + \EdgeInGraphLoop{\cmdGR@cl@prefix}{#2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grLCF +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand{\grLCF}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \setcounter{tkz@gr@a}{#3} + \setcounter{tkz@gr@b}{0} + \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}} + \pgfmathsetcounter{tkz@gr@c}{\thetkz@gr@a * \thetkz@gr@b} + \setcounter{tkz@gr@b}{\thetkz@gr@c} + \grCycle[#1]{\thetkz@gr@c} +%<––––––––––––––––––––––––– End Vertex ––––––––––––––––––––––––––––––––––––> + \pgfmathsetcounter{tkz@gr@a}{#3-1} + \edef\tkz@auxctp{\thetkz@gr@a} + \setcounter{tkz@gr@e}{0} + \foreach \V@k in {0,...,\tkz@auxctp}{% + \foreach \n in {#2}{% + \ifthenelse{\n < 0}{% + \pgfmathsetcounter{tkz@gr@b}{\n+\thetkz@gr@c}}{% + \pgfmathsetcounter{tkz@gr@b}{\n}} + \pgfmathsetcounter{tkz@gr@n}% + {Mod(\thetkz@gr@e+\thetkz@gr@b,\thetkz@gr@c)} + \Edge(\cmdGR@cl@prefix\thetkz@gr@e)(\cmdGR@cl@prefix\thetkz@gr@n) + \stepcounter{tkz@gr@e}% + }% + }% +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grStar +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grStar}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grEmptyStar[#1]{#2} + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \EdgeInGraphFromOneToComp{\cmdGR@cl@prefix}{#2}{\thetkz@gr@p} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grWheel +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grWheel}[2][]{ +\begingroup% + \setkeys[GR]{cl}{#1}% + \grStar[#1]{#2} + \pgfmathsetcounter{tkz@gr@e}{#2-1} + \EdgeInGraphLoop{\cmdGR@cl@prefix}{\thetkz@gr@e} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grSQCircle +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grSQCycle}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{#2}% + \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grLadder +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grLadder}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grPath[#1,RS=0]{#2} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RS} + \grPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPrism +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grPrism}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{#2} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{#2} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCompleteBipartite +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCompleteBipartite}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \pgfmathparse{(\cmdGR@cl@RA * \thetkz@gr@a) /2} + \let\tkzRAxpos\pgfmathresult% + \pgfmathsetcounter{tkz@gr@a}{#3-1} + \pgfmathparse{(\cmdGR@cl@RB * \thetkz@gr@a) /2} + \let\tkzRBxpos\pgfmathresult% + \ifdim\tkzRBxpos pt > \tkzRAxpos pt\relax% + \pgfmathadd{\tkzRBxpos}{-\tkzRAxpos} + \let\tkzaxpos\pgfmathresult% + \def\tkzbxpos{0} + \else% + \pgfmathadd{\tkzRAxpos}{-\tkzRBxpos} + \let\tkzbxpos\pgfmathresult% + \def\tkzaxpos{0} + \fi% + \begin{scope}[xshift=\tkzaxpos cm] + \grEmptyPath[#1,RS=0]{#2} + \end{scope} + \begin{scope}[xshift=\tkzbxpos cm] + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RS} + \edef\tkzb@stemp{\cmdGR@cl@RB} + \grEmptyPath[#1,RA=\tkzb@stemp,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#3} + \end{scope} + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \pgfmathsetcounter{tkz@gr@e}{#3-1} + \edef\tkz@auxctp{\thetkz@gr@e} + \foreach \cpx in {0,...,\tkz@auxctp}{% + \EdgeFromOneToAll{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{\cpx}{#2} + }% +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grTriangularGrid +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grTriangularGrid}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1} + \ifcase\cmdGR@cl@form + \or +%<––––––––––––––––––––– form 1 equilateral triangle ––––––––––––––––––––––––> + \pgfmathsetcounter{tkz@gr@a}{#2-1} + %\pgfmathsetcounter{tkz@gr@b}{#2} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \lg in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@b}{#2-\lg} + \setcounter{tkz@gr@b}{\thetkz@gr@b} + \edef\tkzb@rtemp{\cmdGR@cl@RA} + \edef\tkzb@ptemp{\cmdGR@cl@prefix} + \pgfmathmultiply{\cmdGR@cl@RA}{\lg} + \let\myresult\pgfmathresult + \pgfmathparse{\cmdGR@cl@RA*\lg/2} + \let\tkzaxpos\pgfmathresult + \begin{scope}[xshift=\tkzaxpos cm] + \grPath[#1,% + RA = \tkzb@rtemp,% + RS = \myresult,% + prefix = \tkzb@ptemp,% + num = \lg]{\thetkz@gr@b}% + \end{scope}% + } + \or +%<––––––––––––––––––––––––––– form 2 right triangle ––––––––––––––––––––––––> + \pgfmathsetcounter{tkz@gr@a}{#2-1} + % \pgfmathsetcounter{tkz@gr@b}{#2} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \lg in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@b}{#2-\lg} + \setcounter{tkz@gr@b}{\thetkz@gr@b} + \edef\tkzb@rtemp{\cmdGR@cl@RA} + \edef\tkzb@ptemp{\cmdGR@cl@prefix} + \pgfmathmultiply{\cmdGR@cl@RA}{\lg} + \let\myresult\pgfmathresult + \grPath[#1,% + RA = \tkzb@rtemp,% + RS = \myresult,% + prefix = \tkzb@ptemp,% + num = \lg,form=1]{\thetkz@gr@b}% + } + \or + \pgfmathsetcounter{tkz@gr@a}{#2-1} + \pgfmathsetcounter{tkz@gr@b}{#2} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \lg in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@b}{#2-\lg} + \setcounter{tkz@gr@b}{\thetkz@gr@b} + \edef\tkzb@rtemp{\cmdGR@cl@RA} + \edef\tkzb@ptemp{\cmdGR@cl@prefix} + \pgfmathmultiply{\cmdGR@cl@RA}{\lg} + \let\myresult\pgfmathresult + \begin{scope}[xshift=\myresult cm] + \grPath[#1,% + RA = \tkzb@rtemp,% + RS = \myresult,% + prefix = \tkzb@ptemp,% + num = \lg,form=1]{\thetkz@gr@b}% + \end{scope}% + } + \fi% + \pgfmathsetcounter{tkz@gr@a}{#2-2} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@e}{\thetkz@gr@a-\V@x} + \edef\tkz@auxctpb{\thetkz@gr@e} + \foreach \V@y in {0,...,\tkz@auxctpb}{% + \pgfmathsetcounter{tkz@gr@b}{\V@y+1} + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)% + (\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b) + \pgfmathsetcounter{tkz@gr@p}{\V@x+1} + \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)% + (\cmdGR@cl@prefix\thetkz@gr@p\grLabelSep\V@y) + }% + } +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grHeawood +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grHeawood}[1][]{% #1 options #2 ordre du graphe +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{14} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{14}{5}{0}{2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCirculant #1 option #2 vertex #3 add k +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCirculant}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1} + \grEmptyCycle[#1]{#2}% + \pgfmathisprime{#2}% + \ifnum\pgfmathresult=1\relax + \foreach \kci in {#3}{% + \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci}}% + \else + \foreach \kci in {#3}{% + \pgfmathisfactor{#2}{\kci}% + \ifnum\pgfmathresult=1\relax + \pgfmathsetcounter{tkz@gr@a}{\kci-1} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \start in {0,...,\tkz@auxctp}{% + \setcounter{tkz@gr@i}{\start}% + \setcounter{tkz@gr@n}{#2}% + \whiledo{\not\equal{\value{tkz@gr@n}}{\start}}{% + \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@i+\kci,#2)} + \Edge(\cmdGR@cl@prefix\thetkz@gr@i)% + (\cmdGR@cl@prefix\thetkz@gr@n)% + \pgfmathsetcounter{tkz@gr@i}{\thetkz@gr@n}% + }% + }% + \else + \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci} + \fi + }% + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPetersenG +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grGeneralizedPetersen}[3][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{#2} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@pptemp{\cmdGR@cl@prefixx} + \edef\tkzb@ptemp{\cmdGR@cl@prefix} + \grCirculant[#1,RA=\tkzb@rtemp,prefix=\tkzb@pptemp]{#2}{#3} + \EdgeIdentity{\tkzb@ptemp}{\cmdGR@cl@prefixx}{#2} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPetersen +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grStartwo}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@e}{3*#2-2} + \pgfmathsetcounter{tkz@gr@a}{3*#2-1} + \grEmptyCycle[#1]{\thetkz@gr@a} + \EdgeInGraphMod{\cmdGR@cl@prefix}{\thetkz@gr@a}{#2}% +\endgroup% +} + +\newcommand*{\grPetersen}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grCycle[#1]{5}% + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grStartwo[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{2} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{5} + \or + \grCycle[#1]{6} + \begin{scope}[rotate=30] + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grStar[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4} + \end{scope} + \setcounter{tkz@gr@a}{2} + \foreach \V@x in {0,...,5}{% + \ifthenelse{\equal{\thetkz@gr@a}{-1}}{% + \setcounter{tkz@gr@a}{2}}{% + }% + \Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefixx\thetkz@gr@a) + \addtocounter{tkz@gr@a}{-1}% + }% + \or + \grEmptyStar[#1]{10} + \EdgeInGraphLoop{\cmdGR@cl@prefix}{9} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{9}{4}{0}{3} + \foreach \V@x in {2,5,8}{% + \Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefix 9)}% + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPlatonic +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grTetrahedral}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \begin{scope}[rotate=90] + \grWheel[#1]{4}% + \end{scope} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grOctahedral +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grOctahedral}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grComplete[#1]{3}% + \begin{scope}[rotate=-60] + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grComplete[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{3}% + \end{scope} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{3} + \EdgeMod{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{3}{1} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCubicalGraph +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCubicalGraph}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{4} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4} + \ifcase\cmdGR@cl@form + \or + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{4} + \or + \EdgeMod*{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{4}{1}{2} + \EdgeMod*{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{4}{1}{2} + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grIcosahedral +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grIcosahedral}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grCycle[#1]{6}% + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6}{2} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{6} + \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6}{1} + \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6}{-1} + \or + \grCycle[#1]{3} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6}% + \begin{scope}[rotate=60] + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{3}% + \end{scope} + \setcounter{tkz@gr@a}{2} + \foreach \st in {5,0,1}{% + \foreach \v in {0,1,2}{% + \pgfmathsetcounter{tkz@gr@n}{Mod((\thetkz@gr@a*\v)+\st,6)}% + \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixx\thetkz@gr@n) + }% + }% + \setcounter{tkz@gr@a}{2} + \foreach \v in {0,1,2}{% + \foreach \st in {0,1,2}{% + \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@a*\v+\st,6)}% + \Edge(\cmdGR@cl@prefixxx\v)(\cmdGR@cl@prefixx\thetkz@gr@n) + }% + }% + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grDodecahedral +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grDodecahedral}[1][]{% +\begingroup% +\setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grCycle[#1]{10} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{10}{2} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{10} + \or + \grCycle[#1]{5} + \begin{scope}[rotate=36] + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5} + \end{scope} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5} + \begin{scope}[rotate=36] + \edef\tkzb@rtemp{\cmdGR@cl@RD} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx} + \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5}% + \end{scope} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{5} + \EdgeIdentity{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixxxx}{5} + \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{5} + \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{5}{-1} + \or + \grCycle[#1]{5} + \begin{scope}[rotate=36] + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5} + \end{scope} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{10} + \EdgeInGraphLoop{\cmdGR@cl@prefixxx}{5} + \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}% + {\cmdGR@cl@prefixx}{10}{0}{2}{5} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{5}{0}{1}% + {\cmdGR@cl@prefixx}{10}{1}{2}{5} + \or + \grLCF[#1]{10,7,4,-4,-7,10,-4,7,-7,4}{2} + \or + \grCycle[#1]{10} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6} + \begin{scope}[rotate=45] + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4}% + \end{scope} + \setcounter{tkz@gr@a}{0} + \foreach \v in {1,4,6,9}{% + \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixxx\thetkz@gr@a) + \stepcounter{tkz@gr@a} + }% + \setcounter{tkz@gr@a}{0} + \foreach \v in {2,1,5,4}{% + \Edge(\cmdGR@cl@prefixx\v)(\cmdGR@cl@prefixxx\thetkz@gr@a) + \stepcounter{tkz@gr@a} + }% + \setcounter{tkz@gr@a}{0} + \foreach \v in {0,2,3,5,7,8}{% + \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixx\thetkz@gr@a) + \stepcounter{tkz@gr@a} + }% + \Edge(\cmdGR@cl@prefixxx0)(\cmdGR@cl@prefixxx3) + \Edge(\cmdGR@cl@prefixxx1)(\cmdGR@cl@prefixxx2) + \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixx1) + \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixx5) + \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx2) + \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx4) +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grMobiusKantor +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grMobiusKantor}[1][]{% #1 options #2 ordre du graphe +\begingroup% + \setkeys[GR]{cl}{#1} + \ifcase\cmdGR@cl@form + \or + \grCycle[#1]{16} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{16}{5}{0}{2} + \or + \grCycle[#1]{8} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{8}{3} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{8} + \or + \grCirculant[#1]{8}{3} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{8} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{8} + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grMoebiusLadder +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grMobiusLadder}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1} + \grEmptyCycle[#1]{#2} + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{#2}% + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2} + \EdgeInGraphLoop*{\cmdGR@cl@prefix}{#2} + \EdgeInGraphLoop*{\cmdGR@cl@prefixx}{#2} + \Edge(\cmdGR@cl@prefix0)(\cmdGR@cl@prefixx\thetkz@gr@p) + \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefix\thetkz@gr@p) +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCocktailParty +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCocktailParty}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \grPath[#1,RS=0]{#2} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RS} + \grPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2} + \edef\tkz@auxctp{\thetkz@gr@p} + \foreach \cpx in {0,...,\tkz@auxctp}{% + \EdgeFromOneToComp{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{\cpx}{#2} + } +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grCrown +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grCrown}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@gr@p}{#2-1} + \grEmptyPath[#1,RS=0]{#2} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RS} + \grEmptyPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2} + \edef\tkz@auxctp{\thetkz@gr@p} + \foreach \cpx in {0,...,\thetkz@gr@p}{% + \EdgeFromOneToComp{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{\cpx}{#2} + } +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grMcGee +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grMcGee}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{-12,7,-7}{8} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grRobertson +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grRobertson}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{8,4,7,4,8,5,7,4,7,8,4,5,7,8,4,8,4,8,4}{1} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grRobertsonWegner +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grRobertsonWegner}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{6,12}{15} + \EdgeInGraphMod{\cmdGR@cl@prefix}{30}{9}{1}{6} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{15}{2}{6} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{9}{3}{6} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grDoyle +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grDoyle}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grCycle[#1]{9} + \begin{scope}[rotate=18] + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{9}{2} + \end{scope} + \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{9}{1} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{9}{4} + \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixxx}{9} + \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{9}{1} + \or + \grCycle[#1]{27} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{0}{3} + {\cmdGR@cl@prefix}{27}{13}{3}{9} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{1}{3} + {\cmdGR@cl@prefix}{27}{5}{3}{9} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{0}{3} + {\cmdGR@cl@prefix}{27}{20}{3}{9} + \or + \grCycle[#1]{27} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{17}{1} + {\cmdGR@cl@prefix}{27}{10}{-2}{4} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{26}{1} + {\cmdGR@cl@prefix}{27}{19}{-2}{4} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{8}{1} + {\cmdGR@cl@prefix}{27}{1}{-2}{4} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{4}{1} + {\cmdGR@cl@prefix}{27}{27}{-2}{3} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{8}{1} + {\cmdGR@cl@prefix}{27}{1}{-2}{4} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{14}{1} + {\cmdGR@cl@prefix}{27}{7}{-2}{2} + \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{23}{1} + {\cmdGR@cl@prefix}{27}{16}{-2}{2} + \Edge(\cmdGR@cl@prefix9)(\cmdGR@cl@prefix13)% + \Edge(\cmdGR@cl@prefix18)(\cmdGR@cl@prefix22)% + \fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grDesargues +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grDesargues}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grLCF[#1]{5,-5,9,-9}{5} + \or + \grGeneralizedPetersen[#1]{10}{3} + \fi +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grKonisberg +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% #1 prefix #2 indice #2 prefix #3 indice choisie entre #4 et #5 ... +\newcommand{\grKonisberg}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grCycle[#1]{4} + \Edge[style={bend left}](\cmdGR@cl@prefix1)(\cmdGR@cl@prefix2) + \Edge[style={bend left}](\cmdGR@cl@prefix2)(\cmdGR@cl@prefix3) + \Edge(\cmdGR@cl@prefix0)(\cmdGR@cl@prefix2) +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grWong +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grWong}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{8,4,12,4,8,4}{5} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{15}{0}{3} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{16}{1}{6} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{18}{4}{6} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grTutte +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grTutteCoxeter}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{-13,-9,7,-7,9,13}{5} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grFoster +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grFoster}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{17,-9,37,-37,9,-17}{15} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grFolkman +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grFolkman}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{5,-7,-7,5}{5} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grFranklin +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grFranklin}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{5,-5}{6} +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grNauru +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grNauru}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{5, −9, 7, −7, 9, −5}{4} +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grDick +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grDick}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{5,-5,13,-13}{8} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grHarries +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +\newcommand{\grHarries}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \grLCF[#1]{-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29}{5} +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grAndrasfai +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcounter{tkza@tmp} + \newcommand*{\grAndrasfai}[2][]{% + \begingroup + \setkeys[GR]{cl}{#1}% + \pgfmathsetcounter{tkz@bg@cnt}{3*#2-1} + \grEmptyCycle[#1]{\thetkz@bg@cnt} + \pgfmathsetcounter{tkza@tmp}{\thetkz@bg@cnt/2} + \pgfmathsetcounter{tkza@tmp}{\thetkz@bg@cnt+1} + \pgfmathsetcounter{tkz@gr@p}{1} + \whiledo{\value{tkz@gr@p} < \value{tkza@tmp}}{% + \EdgeInGraphMod*{\cmdGR@cl@prefix}{\thetkz@bg@cnt}{\thetkz@gr@p}{0}{1} + \pgfmathsetcounter{tkz@gr@p}{\thetkz@gr@p+3} + } +\endgroup +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grGrotzsch +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grGrotzsch}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \begin{scope}[rotate=18]% + \grStar[#1]{6}% + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5}% + \Edges(\cmdGR@cl@prefix0,\cmdGR@cl@prefixx1,% + \cmdGR@cl@prefix2,\cmdGR@cl@prefixx3,% + \cmdGR@cl@prefix4,\cmdGR@cl@prefixx0,% + \cmdGR@cl@prefix1,\cmdGR@cl@prefixx2,% + \cmdGR@cl@prefix3,\cmdGR@cl@prefixx4,\cmdGR@cl@prefix0) + \end{scope} + \or + \begin{scope}[rotate=18]% + \grStar[#1]{6}% + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \begin{scope}[rotate=-36]% + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5}{2}% + \end{scope} + \EdgeDoubleMod{a}{5}{0}{1}% + {b}{5}{1}{1}{4} + \EdgeIdentity{a}{b}{5} + \end{scope} +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grLevi +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grLevi}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form + \or + \grLCF[#1]{-13,-9,7,-7,9,13}{5} + \or + \grCycle[#1]{10} + \EdgeInGraphMod{\cmdGR@cl@prefix}{10}{5} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10} + \EdgeInGraphMod{\cmdGR@cl@prefixxx}{10}{4} +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grPappus +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grPappus}[1][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \ifcase\cmdGR@cl@form +\or + \grLCF[#1]{5,7,-7,7,-7,-5}{3} +\or + \begin{scope}[rotate=30]% + \grCycle[#1]{6} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{6}{0}{2}% + {\cmdGR@cl@prefixx}{6}{5}{2}{2} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{6}{5}{2}% + {\cmdGR@cl@prefix}{6}{1}{2}{2} + \EdgeDoubleMod{\cmdGR@cl@prefixx}{6}{0}{2}% + {\cmdGR@cl@prefix}{6}{0}{2}{2} +\end{scope} +\or + \begin{scope}[rotate=30] + \grCycle[#1]{6} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6}{2} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6} + \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6} + \EdgeInGraphMod{\cmdGR@cl@prefixxx}{6}{3} +\end{scope} +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grChvatal +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grChvatal}[1][]{% +\begingroup% +\setkeys[GR]{cl}{#1}% +\ifcase\cmdGR@cl@form +\or + \begin{scope}[rotate=45] + \grCycle[#1]{4} + \end{scope} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \begin{scope}[rotate=22.25] + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{8} + \end{scope} + \EdgeInGraphMod{\cmdGR@cl@prefixx}{8}{4} + \EdgeInGraphMod*{\cmdGR@cl@prefixx}{8}{1}{1}{2} + \EdgeInGraphMod*{\cmdGR@cl@prefixx}{8}{3}{1}{2} + \EdgeDoubleMod{\cmdGR@cl@prefix}{4}{0}{1}% + {\cmdGR@cl@prefixx}{8}{1}{2}{3} + \EdgeDoubleMod{\cmdGR@cl@prefix}{4}{0}{1}% + {\cmdGR@cl@prefixx}{8}{0}{2}{3} +\or + \begin{scope}[rotate=18] + \grCycle[#1]{5} + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5} + \end{scope} + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{2} + \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}% + {\cmdGR@cl@prefixx}{5}{1}{1}{4} + \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}% + {\cmdGR@cl@prefixx}{5}{4}{1}{4} + \EdgeFromOneToSel{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixx}{0}{4,0,1} + \EdgeFromOneToSel{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixx}{1}{1,2,3} + \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx4) + \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixxx1) + \Edge(\cmdGR@cl@prefixx2)(\cmdGR@cl@prefixxx0) +\or + \grCycle[#1]{12} + \Edges(\cmdGR@cl@prefix0,\cmdGR@cl@prefix6,\cmdGR@cl@prefix3,% + \cmdGR@cl@prefix8,\cmdGR@cl@prefix11,\cmdGR@cl@prefix5,% + \cmdGR@cl@prefix2,\cmdGR@cl@prefix9,\cmdGR@cl@prefix0) + \Edges(\cmdGR@cl@prefix1,\cmdGR@cl@prefix7,\cmdGR@cl@prefix10,% + \cmdGR@cl@prefix4,\cmdGR@cl@prefix1) +\fi +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grBalaban +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\newcommand*{\grBalaban}[1][]{% +\begingroup% +\setkeys[GR]{cl}{#1}% +\ifcase\cmdGR@cl@form +\or + \grCycle[#1]{50} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{50}{9}{3}{5} + \EdgeInGraphMod*{\cmdGR@cl@prefix}{50}{25}{0}{5} + \begin{scope}[rotate=12] + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}{3} + \end{scope} + \begin{scope}[rotate=24] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}{3} + \end{scope} + \EdgeDoubleMod{\cmdGR@cl@prefix}{50}{1}{5}% + {\cmdGR@cl@prefixx}{10}{0}{1}{10} + \EdgeDoubleMod{\cmdGR@cl@prefix}{50}{4}{5}% + {\cmdGR@cl@prefixxx}{10}{0}{1}{10} +\or + \begin{scope}[rotate=9] + \grCycle[#1]{10} + \end{scope} + \begin{scope}[rotate=-9] + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10} + \end{scope} + \begin{scope}[rotate=6] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{30} + \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{1}{0}{3} + \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{1}{1}{3} + \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{15}{1}{3} + \end{scope} + \begin{scope}[rotate=9] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx} + \edef\tkzb@rtemp{\cmdGR@cl@RD} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20} + \EdgeInGraphMod*{\cmdGR@cl@prefixxxx}{20}{7}{0}{2} + \EdgeInGraphMod*{\cmdGR@cl@prefixxxx}{20}{5}{1}{2} + \end{scope} + \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1} + {\cmdGR@cl@prefixxx}{30}{0}{3}{9} + \EdgeDoubleMod{\cmdGR@cl@prefixx}{10}{0}{1}% + {\cmdGR@cl@prefixxx}{30}{29}{3}{9} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{30}{0}{3}% + {\cmdGR@cl@prefixxxx}{20}{0}{2}{9} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{30}{2}{3}% + {\cmdGR@cl@prefixxxx}{20}{1}{2}{9} +\or +\grEmptyCycle[#1]{10} +\begin{scope}[rotate=9] + \edef\tkzb@ptemp{\cmdGR@cl@prefixx} + \edef\tkzb@rtemp{\cmdGR@cl@RB} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20} +\end{scope} +\begin{scope}[rotate=13] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxx} + \edef\tkzb@rtemp{\cmdGR@cl@RC} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10} +\end{scope} +\begin{scope}[rotate=-13] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx} + \edef\tkzb@rtemp{\cmdGR@cl@RD} + \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10} +\end{scope} +\begin{scope}[rotate=9] + \edef\tkzb@ptemp{\cmdGR@cl@prefixxxxx} + \edef\tkzb@rtemp{\cmdGR@cl@RE} + \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20}{6} +\end{scope} + \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxxxx}{20} + \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1}% + {\cmdGR@cl@prefixx}{20}{0}{2}{10} + \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1}% + {\cmdGR@cl@prefixx}{20}{19}{2}{10} + \EdgeInGraphMod{\cmdGR@cl@prefix}{10}{5} + \EdgeDoubleMod{\cmdGR@cl@prefixxx}{10}{0}{1}% + {\cmdGR@cl@prefixx}{20}{0}{2}{10} + \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{0}{1}% + {\cmdGR@cl@prefixx}{20}{19}{2}{10} + \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{0}{1}% + {\cmdGR@cl@prefixxx}{10}{1}{1}{10} + \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{1}{1}% + {\cmdGR@cl@prefixxx}{10}{0}{1}{10} +\fi +\endgroup% +} +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% Labels +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> + +% #2 label/prefix/num +\define@cmdkey [GR] {WL} {color}[black]{} +\define@cmdkey [GR] {WL} {labelstyle}{} +\define@cmdkey [GR] {WL} {size}{} +\define@cmdkey [GR] {WL} {style}{} +\presetkeys [GR] {WL} {color = black,% + labelstyle = {},% + size = {},% + style = {}}{} +\newcommand{\grWriteExplicitLabels}[2][]{% +\begingroup% + \setkeys[GR]{WL}{#1}% + \foreach \text/\where in {#2}{% + \node at (\where) {\text}; + }% +\endgroup% +} +\newcommand{\grWriteExplicitLabel}[2][]{% +\begingroup% + \setkeys[GR]{cl}{#1}% + \node at (\where) {\text}; +\endgroup% +}% +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% AssignVertexLabel +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\tikzset{AssignStyle/.style={}} +\define@cmdkey [GR] {AVL} {color}{} +\define@cmdkey [GR] {AVL} {size}{} +\define@cmdkey [GR] {AVL} {mathsize}{} +\define@boolkey[GR] {AVL} {Math}[true]{} +\presetkeys [GR] {AVL} {size = \normalsize,% + mathsize = \displaystyle,% + color = black,% + Math = false}{} \newcommand*{\AssignVertexLabel}[3][]{% +\begingroup% + \setkeys[GR]{AVL}{#1} + \foreach \name [count=\xi from 0] in {#3}{% + \ifGR@AVL@Math% + \node at (#2\xi) + {$\textcolor{\cmdGR@AVL@color}{\cmdGR@AVL@mathsize\name}$}; + \else + \node[AssignStyle] at (#2\xi) + {\textcolor{\cmdGR@AVL@color}{\cmdGR@AVL@size\name}}; + \fi} + +\endgroup% +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% grEdgeForTree +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% #1 prefix #2 indice #2 prefix #3 indice choisie entre #4 et #5 ... +\newcommand{\grEdgeForTree}[5]{% +\begingroup% + \foreach \V@x in {#4,...,#5}{% + \Edge(#1#2)(#3\V@x)% + }% +\endgroup% +} + +\newcommand{\grSubtreeOfCage}[3][]{% + \begingroup + \setkeys[GR]{cl}{#1}% + \edef\tkzb@rtemp{\cmdGR@cl@RA} + \edef\tkzb@rtempx{\cmdGR@cl@RB} + \edef\tkzb@ptemp{\cmdGR@cl@prefix} + \ifthenelse{\isodd{#3}}% + % odd girth + {% + \pgfmathsetcounter{tkz@gr@a}{(#3-3)/2} + \Vertex{\cmdGR@cl@prefix 0\grLabelSep 0} + \edef\tkz@auxctp{\thetkz@gr@a} + \foreach \V@x in {0,...,\tkz@auxctp}{% + \pgfmathsetcounter{tkz@gr@b}{#2*((#2-1)^\V@x)}% + \pgfmathsetmacro{\sep@path}{\tkzb@rtemp/((#2-1)^\V@x)}% + \pgfmathsetmacro{\y@h}{\tkzb@rtempx*(\V@x+1)}% + \pgfmathsetcounter{tkz@gr@c}{\V@x+1}% + \grEmptyPath[% + prefix=\tkzb@ptemp\thetkz@gr@c\grLabelSep, + form=2, + RA=\sep@path, + x=0, + y=\y@h]{\thetkz@gr@b}% + }% + % edges from the root of the tree + \EdgeFromOneToAll{\tkzb@ptemp0\grLabelSep}% + {\tkzb@ptemp1\grLabelSep}{0}{#2} + % ca = levels from where extra edges emerge + % cb = edges per vertex + \pgfmathsetcounter{tkz@gr@a}{\thetkz@gr@a-1} +\edef\tkz@auxctpa{\thetkz@gr@a} + \foreach \V@y in {0,...,\tkz@auxctpa}{% + \pgfmathsetcounter{tkz@gr@b}{#2*(#2-1)^\V@y-1} +\edef\tkz@auxctpb{\thetkz@gr@b} + \foreach \a in {0,...,\tkz@auxctpb}{% + \pgfmathsetcounter{tkz@gr@c}{\a*(#2-1)}% + \pgfmathsetcounter{tkz@gr@d}{\a*(#2-1)+(#2-2)}% + \pgfmathsetcounter{tkz@gr@ta}{\V@y+1} + \pgfmathsetcounter{tkz@gr@tb}{\V@y+2} + \EdgeFromOneToSeq{\tkzb@ptemp\thetkz@gr@ta\grLabelSep}% + {\tkzb@ptemp\thetkz@gr@tb\grLabelSep}{\a}% + {\thetkz@gr@c}{\thetkz@gr@d} + }% + }% + }% + % even girth + {% + \pgfmathsetcounter{tkz@gr@a}{(#3-2)/2} + \foreach \V@x in {0,...,\thetkz@gr@a}{% + \pgfmathsetcounter{tkz@gr@b}{2*((#2-1)^\V@x)}% + \pgfmathsetmacro{\sep@path}{\tkzb@rtemp/((#2-1)^\V@x)}% + \pgfmathsetmacro{\y@h}{\tkzb@rtempx*\V@x}% + \pgfmathsetcounter{tkz@gr@c}{\V@x}% + \grEmptyPath[% + prefix=\tkzb@ptemp\thetkz@gr@c\grLabelSep, + form=2, + RA=\sep@path, + x=0, + y=\y@h]{\thetkz@gr@b}% + }% + %%%%% + \Edge% + (\tkzb@ptemp0\grLabelSep0)% + (\tkzb@ptemp0\grLabelSep1) + %%%% + \pgfmathsetcounter{tkz@gr@a}{\thetkz@gr@a-1} + \foreach \V@y in {0,...,\thetkz@gr@a}{% + \pgfmathsetcounter{tkz@gr@b}{2*(#2-1)^\V@y-1} + \foreach \a in {0,...,\thetkz@gr@b}{% + \pgfmathsetcounter{tkz@gr@c}{\a*(#2-1)}% + \pgfmathsetcounter{tkz@gr@d}{\a*(#2-1)+(#2-2)}% + \pgfmathsetcounter{tkz@gr@ta}{\V@y} + \pgfmathsetcounter{tkz@gr@tb}{\V@y+1} + \EdgeFromOneToSeq{\tkzb@ptemp\thetkz@gr@ta\grLabelSep}% + {\tkzb@ptemp\thetkz@gr@tb\grLabelSep}{\a}% + {\thetkz@gr@c}{\thetkz@gr@d} + }% + }% + }% + \endgroup +} + +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +% The End +%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\catcode`\@=\tkzAtCode\relax +\endinput diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index b6ca6d843ad..8f157bcc15b 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -758,7 +758,7 @@ my @TLP_working = qw( tikztosvg tile-graphic timbreicmc times timetable timing-diagrams tinos tipa tipa-de tipfr titlecaps titlefoot titlepages titlepic titleref titlesec titling - tkz-base tkz-doc tkz-euclide tkz-fct tkz-graph tkz-tab + tkz-base tkz-berge tkz-doc tkz-euclide tkz-fct tkz-graph tkz-tab tkz-orm tikz-page tlc-article tlc2 tlcockpit tlmgrbasics tocbibind tocdata tocloft tocvsec2 todo todonotes diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds index 79ef372b00a..6558946ffc7 100755 --- a/Master/tlpkg/libexec/ctan2tds +++ b/Master/tlpkg/libexec/ctan2tds @@ -1653,6 +1653,7 @@ chomp (my $ctan_root = `tlpkginfo --ctan-root`); 'thumbpdf' => '&POST_preserve_man', 'tikz-cd' => '&POSTtikz_cd', 'tipa-de' => '&POST_rmsymlink', + 'tkz-berge' => '&POSTtkz_berge', 'tlcockpit' => '&POST_do_man', 'tudscr' => '&POSTtudscr', 'uplatex' => '&POST_preserve_man', @@ -7010,6 +7011,11 @@ sub POSTtikz_cd { &mv_with_mkdir ("latex/tikz-cd/tikzlibrary*tex", "generic/tikz-cd/"); } +sub POSTtkz_berge { + print "POST$package - latex/* to runtime\n"; + &mv_with_mkdir ("latex/*", "$DEST/tex/latex/$package"); +} + sub POSTtudscr { print "POST$package - subdirs\n"; &xchdir (".."); # cd back from the prehook diff --git a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc index 7395c7073f4..87ca90fe57a 100644 --- a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc @@ -195,6 +195,7 @@ depend tile-graphic depend timing-diagrams depend tipfr depend tkz-base +depend tkz-berge depend tkz-doc depend tkz-euclide depend tkz-fct diff --git a/Master/tlpkg/tlpsrc/tkz-berge.tlpsrc b/Master/tlpkg/tlpsrc/tkz-berge.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d --- /dev/null +++ b/Master/tlpkg/tlpsrc/tkz-berge.tlpsrc |