Does it exist any program (for linux) which can generate a nice Cayley graph of any $\mathbb Z_n$? (If it's possible to create such a graph at all, that is.)
(where perhaps $n ≤ 100$ or something like that)
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Martin Sleziak
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John Smith
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1You can generate Cayley graphs with the GRAPE package of GAP. – Albert Steppi Dec 05 '13 at 15:01
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2The Cayley graph for $\mathbb{Z}_n$ with the standard generator is fairly boring, is it not? – ronno Dec 05 '13 at 15:09
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@AlbertSteppi Thank you very much, I will try it out. – John Smith Dec 05 '13 at 15:18
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@ronno Well, I find the Cayley graphs of $\mathbb Z_6$ and $\mathbb Z_8$ kind of nice. Perhaps not mindblowing but neat. – John Smith Dec 05 '13 at 15:20
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Is $\mathbb Z_n$ the group of integers modulo $n$, or something else? – Cheerful Parsnip Dec 05 '13 at 15:49
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@GrumpyParsnip Yes I mean the good old lovely group of integers mod n. I should perhaps have specified this. – John Smith Dec 05 '13 at 15:51
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@JohnSmith: if you take the standard generator, then is the Cayley graph not just an $n$-gon? – Cheerful Parsnip Dec 05 '13 at 16:03
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3@GrumpyParsnip Ah, yes of course. $<1>$ of $\mathbb Z_n$ isn't very awesome. I'm more interested in generating graphs using not only the standard generator but two or more. Like this http://terrytao.files.wordpress.com/2010/07/s31.png for $\mathbb Z_6$ using the generating set ${2,3}$. – John Smith Dec 05 '13 at 16:31
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@JohnSmith: Okay that makes more sense now. – Cheerful Parsnip Dec 05 '13 at 17:08
1 Answers
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In SageMath: g=graphs.CirculantGraph(8,[1,4,7])
First argument is the number of vertices, second is the connection set. Now
g.show() produces a drawing.
andselisk
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Chris Godsil
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