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.



Enumeration of Regular Graphs
I think the answer is no, but I would consult the following link:


<http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html>


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.


