# how to Compute the number of pairwise non-isomorphic 7-regular graphs on 10 vertices?

Compute the number of pairwise non-isomorphic 7-regular graphs on 10 vertices?

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What have you tried? Also, it is usually best not to phrase your question in the form of a command. The question may be to compute something, but you're basically telling us to do it for you. At least say, "I'm stuck on this, can any one please help?" or something like that. – Graphth Oct 20 '12 at 14:14

You do that by looking at the complement, the graph of missing edges.

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If you're interested in this question from a computational mathematics point of view (and this is a specific instance of a broader problem), then this can be computed using Brendan McKay's geng (part of the gtools package, which can be downloaded with nauty). Specifically:

geng -n 10 -d7 -D7


computes the number of non-isomorphic graphs with $10$ vertices, minimum degree $7$ and maximum degree $7$.

If you want to understand why the number is what it is, Hendrik Jan's hint is excellent.

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