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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-Coxeter.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
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+\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