Counts of labelled simple regular graphs

This page is an appendix to the paper Asymptotic enumeration of graph factors by cumulant expansion, by Mikhail Isaev and Brendan D. McKay.

Define RG(n,d) to be the number of labelled simple regular graphs (not necessarily connected) with n vertices and degree d.

The Maple input text file RGvals.maple contains a large number of exact values, which are readable even if you don't know Maple.

There are also the following procedures:

RG(n,d) gives the exact value of RG(n,d) if it is known. Otherwise, it returns unevaluated.
CRG(n,d) gives the exact number of connected labelled simple regular graphs if it is known. Otherwise, it returns unevaluated.
Maxn(d) gives the largest n for which RG(n,d) is known. In the case of d≤4, all values are known, in which case the function returns 1000.
RGest(n,d) returns an estimate of RG(n,d), plus an interval conjectured to contain the exact value for n≥10. Note that this conjecture has not been proved and no guarantees are made.

Page Master: Brendan McKay, brendan.mckay@anu.edu.au