Example: Star graph

Published 2008-11-20 | Author: Anthony Labarre

The star graph of order n has the set of all permutations of {1,2,…,n} as vertex set and has an edge between any two vertices such that the corresponding permutations can be obtained from one another by swapping the first element with any other element (e.g. (1 2 3 4) will be connected to (3 2 1 4)). This drawing shows the star graph of order 4.

Note. You can find many examples of beautiful graphs in Anthony Labarre’s publications (especially his PhD thesis). Almost all of the graphs have been drawn using TikZ.

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Star graph

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Oder frag auf Deutsch auf TeXwelt.de. En français: TeXnique.fr.

% Star graph
% Author: Anthony Labarre <http://homepages.ulb.ac.be/~alabarre/home.html>
\documentclass{minimal}

\usepackage{tikz}
\newcommand{\LD}{\langle}
\newcommand{\RD}{\rangle}

\begin{document}

\begin{center}
\begin{tikzpicture}
    \tikzstyle{every node}=[draw,circle,fill=white,minimum size=4pt,
                            inner sep=0pt]

    % First, draw the inner hexagon with a ``pin'' -- namely, (3214)
    \draw (0,0) node (1234) [label=left:$\LD 1\ 2\ 3\ 4\RD$] {}
        -- ++(0:2.0cm) node (2134) [label=right:$\LD 2\ 1\ 3\ 4\RD$] {}
        -- ++(300:2.0cm) node (4132) [label=left:$\LD 4\ 1\ 3\ 2\RD$] {}
        -- ++(240:2.0cm) node (1432) [label=right:$\LD 1\ 4\ 3\ 2\RD$] {}
        -- ++(180:2.0cm) node (2431) [label=left:$\LD 2\ 4\ 3\ 1\RD$] {}
        -- ++(120:2.0cm) node (4231) [label=right:$\LD 4\ 2\ 3\ 1\RD$] {}
        -- (1234) % shape is closed, we now connect it to an outer vertex:
        -- ++(120:2.0cm) node (3214) [label=120:$\LD 3\ 2\ 1\ 4\RD$] {};

    % Second, draw the ``outer backbone''
    \draw (3214)
        -- ++(60:2.0cm) node (2314) [label=left:$\LD 2\ 3\ 1\ 4\RD$] {}
        -- ++(0:2.0cm) node (1324) [label=right:$\LD 1\ 3\ 2\ 4\RD$] {}
        -- ++(300:2.0cm) node (3124) [label=60:$\LD 3\ 1\ 2\ 4\RD$] {}
        -- ++(0:2.0cm) node (4123) [label=right:$\LD 4\ 1\ 2\ 3\RD$] {}
        -- ++(300:2.0cm) node (2143) [label=right:$\LD 2\ 1\ 4\ 3\RD$] {}
        -- ++(240:2.0cm) node (3142) [label=right:$\LD 3\ 1\ 4\ 2\RD$] {}
        -- ++(300:2.0cm) node (1342) [label=right:$\LD 1\ 3\ 4\ 2\RD$] {}
        -- ++(240:2.0cm) node (4312) [label=right:$\LD 4\ 3\ 1\ 2\RD$] {}
        -- ++(180:2.0cm) node (3412) [label=-60:$\LD 3\ 4\ 1\ 2\RD$] {}
        -- ++(240:2.0cm) node (2413) [label=right:$\LD 2\ 4\ 1\ 3\RD$] {}
        -- ++(180:2.0cm) node (1423) [label=left:$\LD 1\ 4\ 2\ 3\RD$] {}
        -- ++(120:2.0cm) node (3421) [label=-120:$\LD 3\ 4\ 2\ 1\RD$] {}
        -- ++(180:2.0cm) node (4321) [label=left:$\LD 4\ 3\ 2\ 1\RD$] {}
        -- ++(120:2.0cm) node (2341) [label=left:$\LD 2\ 3\ 4\ 1\RD$] {}
        -- ++(60:2.0cm) node (3241) [label=left:$\LD 3\ 2\ 4\ 1\RD$] {}
        -- ++(120:2.0cm) node (1243) [label=left:$\LD 1\ 2\ 4\ 3\RD$] {}
        -- ++(60:2.0cm) node (4213) [label=left:$\LD 4\ 2\ 1\ 3\RD$] {}
        -- (3214);

    % Add missing ``straight'' edges
    \draw (3241) -- (4231);
    \draw (3421) -- (2431);
    \draw (1432) -- (3412);
    \draw (4132) -- (3142);
    \draw (2134) -- (3124);

    % And finally, add missing ``curved'' edges
    \draw (2341) to [out=-35,in=215] (1342);
    \draw (1243) to [out=35,in=-215] (2143);
    \draw (4123) to [out=270,in=30] (1423);
    \draw (2314) to [out=-30,in=90] (4312);
    \draw (1324) to [out=210,in=90] (4321);
    \draw (4213) to [out=270,in=150] (2413);

\end{tikzpicture}
\end{center}

\end{document}

Comments

  • #1 Kjell Magne Fauske, November 26, 2008 at 2:08 p.m.

    FYI: David Eppstein has written an entry on his weblog about this graph. He calls it a Nauru graph. It is an interesting read.

  • #2 zayesha, September 18, 2013 at 9:53 a.m.

    the above information really helps me a lot bt i still need some more info. about star graph topoloy as itzz a really very vast topic...so can u plzz send me how to draw star graph in c graphics......plzz itzz urgent....nd i really need it.for completing my project

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