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-\newpage\section{Franklin}\label{franklin}
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––– Franklin ––––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-\begin{NewMacroBox}{grFranklin}{\oarg{options}}
-
-\medskip
-From MathWord : \url{http://mathworld.wolfram.com/FranklinGraph.html}
-
-\emph{The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus providing the sole counterexample to the Heawood conjecture.}
-\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
-The Franklin graph is implemented in \tkzname{tkz-berge} as \tkzcname{grFranklin}.
-\end{NewMacroBox}
-
-\tikzstyle{VertexStyle} = [shape = circle,%
- color = white,
- fill = black,
- very thin,
- inner sep = 0pt,%
- minimum size = 18pt,
- draw]
-\tikzstyle{EdgeStyle} = [thick,%
- double = brown,%
- double distance = 1pt]
-\newcounter{tempi}\setcounter{tempi}{0}
-
-\subsection{\tkzname{The Franklin graph : embedding 1}}
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}[scale=.7]
- \grFranklin[Math,RA=7]
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-\vfill\newpage
-\subsection{\tkzname{The Franklin graph : embedding 2}}
-
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}
- \grCycle[Math,RA=4,prefix=a]{6}
- \grCycle[Math,RA=6,prefix=b]{6}
- \foreach \x in {0,...,5}{%
- \ifthenelse{\isodd{\x}}{%
- \pgfmathsetcounter{tempi}{\x-1}}{%
- \pgfmathsetcounter{tempi}{\x+1}}
- \Edge(a\x)(b\thetempi)
-}
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-
-\vfill\newpage
-\subsection{\tkzname{The Franklin graph : with LCF notation embedding 3}}
-
-\space*{2cm}
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}
- \grLCF[Math,RA=7]{-5,-3,3,5}{3}
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-\endinput