From e1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Fri, 22 Jan 2021 03:00:46 +0000 Subject: CTAN sync 202101220300 --- .../NamedGraphs/doc/latex/NamedGraphs-Moebius.tex | 167 +++++++++++++++++++++ 1 file changed, 167 insertions(+) create mode 100644 macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex (limited to 'macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex') diff --git a/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex b/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex new file mode 100644 index 0000000000..111d503453 --- /dev/null +++ b/macros/latex/contrib/tkz/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 -- cgit v1.2.3