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 ofRG(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