A014382 - OEIS (original) (raw)

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 540, 805579, 2585136741, 9799685588961, 42700033549946255, 214755319657939505396, 1251392240942040452186675, 8462215143144463851848329660, 66398444413512642732641312352087, 603696608755863722277922645973602843, 6346188247029220928621633703157327186101

COMMENTS

Since the nontrivial 10-regular graph with the least number of vertices is K_11, there are no disconnected 10-regular graphs with less than 22 vertices. Thus for n<22 this sequence also gives the number of all 10-regular graphs on n vertices. - Jason Kimberley, Sep 25 2009

REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 648.

I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.

EXAMPLE

The null graph on 0 vertices is vacuously connected and 10-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Feb 10 2011

CROSSREFS

10-regular simple graphs: this sequence (connected), A185203 (disconnected).

Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), this sequence (k=10), A014384 (k=11).