Fix numbers n,k. Is there a closed formula known for the number of k-regular graphs consisting of n edges? I have a method of enumerating k-regular graphs on n edges, and would like to have a number to compare the algorithm against.

  • 1
    $\begingroup$ I don't think there's any closed form formula, but you can compare your results with the data in OEIS, such as here: oeis.org/A005638 (for 3-regular graphs) or here: oeis.org/A051031. This is indexed by the number of vertices, not edges, but of course for fixed k this is the same up to a factor of k/2. $\endgroup$
    – Alon Amit
    Apr 21, 2010 at 18:44
  • $\begingroup$ See the answers to this question mathoverflow.net/questions/77730/… $\endgroup$
    – j.c.
    Jun 16, 2018 at 3:23
  • $\begingroup$ @Gwyn Whieldon Is it possible to access your work some how ? $\endgroup$
    – SagarM
    Apr 17, 2021 at 15:00

1 Answer 1


I think the answer is no, but I would consult the following link:


which contains tables of the sums of the numbers you are interested in. The author is very generous with sharing data that is not posted online.


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