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Diffstat (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex')
-rw-r--r-- | obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex new file mode 100644 index 0000000000..b7f5bc4d66 --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Franklin.tex @@ -0,0 +1,71 @@ +\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 |