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author | Norbert Preining <norbert@preining.info> | 2021-01-22 03:00:46 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2021-01-22 03:00:46 +0000 |
commit | e1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 (patch) | |
tree | d2bbebcdb7bcb8fe013a9d3cbd2cff880b18afbf /obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex | |
parent | 37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff) |
CTAN sync 202101220300
Diffstat (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex')
-rw-r--r-- | obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex | 41 |
1 files changed, 0 insertions, 41 deletions
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 deleted file mode 100644 index 4e77e63bd2..0000000000 --- a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Hypercube.tex +++ /dev/null @@ -1,41 +0,0 @@ -\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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