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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-Heawood.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
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+\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}[scale=.75]
+ \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 \ No newline at end of file