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diff --git a/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex b/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex deleted file mode 100644 index b0d5053f6f..0000000000 --- a/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex +++ /dev/null @@ -1,79 +0,0 @@ -\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
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