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diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex new file mode 100644 index 0000000000..c93a1c99ac --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Heawood.tex @@ -0,0 +1,47 @@ +\newpage\section{Heawood graph}\label{heawood} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––– HEAWOOD ––––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +\begin{NewMacroBox}{grHeawood}{\oarg{options}} + +\medskip +From Wikipedia \url{http://en.wikipedia.org/wiki/Heawood_graph} + +\emph{The Heawood graph is an undirected graph with 14 vertices and 21 edges. Each vertex is adjacent to exactly three edges (that is, it is a cubic graph), and all cycles in the graph have six or more edges. Percy John Heawood (1861-1955) was an English mathematician who spent a large amount of time on questions related to the four colour theorem.} + +\medskip +From MathWorld \url{http://mathworld.wolfram.com/HeawoodGraph.html} + +\emph{The Heawood graph is the unique $(3,6)$-cage graph and Moore graph and is graph illustrated below in one of his embeddings.} +\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{Heawood graph}} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Shade] + \grHeawood[RA=7] + \end{tikzpicture} +\end{tkzexample} +\end{center} + +\vfill\newpage +It can be represented in LCF notation as $\big[5,-5\big]^7$ + +\tkzcname{grLCF[RA=5]\{5,9\}\{7\}} gives the result because $-5 = 9\ mod\ 14$. + +\subsection{\tkzname{Heawood graph with LCF notation}}\label{lcf2} +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}% + \GraphInit[vstyle=Art] + \grLCF[RA=7]{5,9}{7}% + \end{tikzpicture} +\end{tkzexample} +\end{center} + + +\vfill\endinput
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