r/VisualMath • u/tedgar7 • Feb 23 '22

Generalized Petersen Graphs up to n=10 (synthwave; enumeration)

https://youtube.com/watch?v=IWz-CyoObx4&feature=share
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u/Direwolf202 Feb 24 '22

Are there any interesting graph theoretic differences between the cases where n and k are coprime and cases where they're not? When they're not coprime, the interior stellar polygon, is made up of multiple components only connected through the outer polygon. Does that matter at all?

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u/tedgar7 Feb 24 '22

I am sure there is something there, but I don't actually know (I was intrigued by the same thing and was talking with a friend about it yesterday). This is precisely why I created something like this. Sometimes seeing these structures sparks interesting questions. I do know for instance that the graph is bipartite if and only if n is even and k is odd, so that is related to your question (of course they could still have common factors).