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A labeling of the Petersen graph

February 26, 2010

The Petersen graph as {\overline{L(K_{5})}}.

\begin{tikzpicture}[rotate=90]
  \newcommand{\aset}[2]{$\{#1,#2\}$}
  \GraphInit[vstyle=Empty]
  \SetVertexNoLabel
  \SetUpVertex[MinSize=20pt]
  \grPetersen[RA=3,RB=1.5]
  \AssignVertexLabel{a}{\aset{1}{2},\aset{3}{4},\aset{1}{5},\aset{2}{3},\aset{4}{5}}
  \AssignVertexLabel{b}{\aset{3}{5},\aset{2}{5},\aset{2}{4},\aset{1}{4},\aset{1}{3}}
\end{tikzpicture}

UPDATE (June 20, 2011): I have modified the source a little so that it works with the last versions of tkz-graph and tkz-berge (the macro \AssignVertexLabel now has only two parameters). Thanks to Alain Matthes for letting me know!

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6 Comments leave one →
  1. Esteban permalink
    June 24, 2010 11:36 pm

    Hi! The /grTriangularGrid method seems to be having conflict with the /AssignVertexLabel command… I trying to rename my nodes on a Hajos generated graph and it seems to skip the “;” from the default labeling.

    Any advice?

    Thanks!

    • Rafael permalink*
      June 25, 2010 9:46 pm

      Yes, the triangular grid graph has a different default way to tag its vertices. I guess in your case I would construct the graph by using several paths and then defining explicitly the rest of the edges.

  2. Allan permalink
    December 24, 2010 5:27 am

    May I have permission to use this figure in a paper that I am writing?

  3. Bojana Juric permalink
    March 9, 2011 1:08 pm

    I would ask, how many possible labelings has the Petersen graph?

    • Allan permalink
      March 10, 2011 8:25 pm

      What sort of labelings do you mean?

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