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What's the simplest way to compute the genus of a graph using Mathematica? I have looked for a Genus function (even in the Combinatorica package), but I don't think there is one.

Note: Efficiency is not an issue for the moment. I am asking for a way to compute the genus, any way, preferably a simple way.

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closed as too broad by Öskå, bobthechemist, rasher, m_goldberg, belisarius Jun 21 at 4:14

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

Related: mathematica.stackexchange.com/q/5381/5 It probably doesn't work for Graph objects, but maybe you could adapt it for your use –  rm -rf Jun 3 '12 at 2:27
Can you point point to some algorithms? BTW, some built-in data have this information: GraphData[{"Complete", 12}, "Genus"] or GraphData["IcosahedralGraph", "Genus"]. And for some classes there are analytic closed formulas: mathworld.wolfram.com/GraphGenus.html –  Vitaliy Kaurov Jun 3 '12 at 4:07
@VitaliyKaurov I know there are algorithms for this, but they are complicated and it will take me some time learn them. I was hoping that using some of Mathematica already implemented methods could ease the job. For instance, my first thought was that Mathematica would have a Genus method somewhere, but that didn't work :) –  becko Jun 5 '12 at 2:57
Have you seen this article? –  J. M. Sep 9 '12 at 17:57
@J.M. I had not seen it. Thanks for pointing it out. –  becko Sep 10 '12 at 21:28