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diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex new file mode 100644 index 0000000000..4e77e63bd2 --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex @@ -0,0 +1,41 @@ +\newpage\section{Hypercube} +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +%<–––––––––––––––––––– Hypercube –––––––––––––––––––––––––––––––> +%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> +From Wikipedia :\url{http://en.wikipedia.org/wiki/Hypercube_graph} + +In the mathematical field of graph theory, the hypercube graph $Q_n$ is a special regular graph with $2n$ vertices, which correspond to the subsets of a set with $n$ elements. Two vertices labelled by subsets S and T are joined by an edge if and only if S can be obtained from T by adding or removing a single element. Each vertex of $Q_n$ is incident to exactly $n$ edges (that is, $Q_n$ is $n$-regular), so the total number of edges is $2^{n-1}n$. +The name comes from the fact that the hypercube graph is the one-dimensional skeleton of the geometric hypercube. +Hypercube graphs should not be confused with cubic graphs, which are graphs that are 3-regular. The only hypercube that is a cubic graph is $Q_3$. + +\tikzstyle{VertexStyle} = [shape = circle,% + fill = red,% + inner sep = 3pt,% + outer sep = 0pt,% + draw] +\SetVertexNoLabel + +\subsection{\tkzname{The hypercube graph $Q_4$} } + +The code is on the next page. + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture} + \grCycle[RA=8]{8} + \pgfmathparse{8*(1-4*sin(22.5)*sin(22.5))} + \let\tkzbradius\pgfmathresult + \grCirculant[prefix=b,RA=\tkzbradius]{8}{3} + \makeatletter + \foreach \vx in {0,...,7}{% + \pgfmathsetcounter{tkz@gr@n}{mod(\vx+1,8)} + \pgfmathsetcounter{tkz@gr@a}{mod(\vx+7,8)} + \pgfmathsetcounter{tkz@gr@b}{mod(\thetkz@gr@n+1,8)} + \Edge(a\thetkz@gr@n)(b\thetkz@gr@b) + \Edge(b\thetkz@gr@a)(a\vx) + } + \makeatother +\end{tikzpicture} +\end{tkzexample} +\end{center} +\endinput
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