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authorNorbert Preining <norbert@preining.info>2021-01-22 03:00:46 +0000
committerNorbert Preining <norbert@preining.info>2021-01-22 03:00:46 +0000
commite1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 (patch)
treed2bbebcdb7bcb8fe013a9d3cbd2cff880b18afbf /macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Tutte.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
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+\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