From e1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Fri, 22 Jan 2021 03:00:46 +0000
Subject: CTAN sync 202101220300

---
 .../NamedGraphs/doc/latex/NamedGraphs-Moebius.tex  | 167 +++++++++++++++++++++
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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
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+++ b/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Moebius.tex
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+\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
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