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\newpage\section{Hypercube}
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%<–––––––––––––––––––– Hypercube –––––––––––––––––––––––––––––––>
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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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