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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 /obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
CTAN sync 202101220300
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-\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 \ No newline at end of file