From 877268a0de707a979be934d888518f6cc02d73a6 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Tue, 10 Mar 2020 03:01:27 +0000 Subject: CTAN sync 202003100301 --- .../NamedGraphs/doc/latex/NamedGraphs-Levi.tex | 79 ++++++++++++++++++++++ 1 file changed, 79 insertions(+) create mode 100644 obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex') diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex new file mode 100644 index 0000000000..b0d5053f6f --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/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 -- cgit v1.2.3