A014382 Number of connected regular graphs of degree 10 with n nodes.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard

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

Examples

			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
		

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.

Links

• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs
• M. Meringer, Fast Generation of Regular Graphs and Construction of Cages, Journal of Graph Theory, 30 (1999), 137-146.
• Eric Weisstein's World of Mathematics, Regular Graph.

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).

Extensions

Using the symmetry of A051031, a(16) and a(17) from Jason Kimberley, Sep 25 2009 and Jan 03 2011

a(18)-a(21) from Andrew Howroyd, Mar 13 2020

a(22)-a(24) from Andrew Howroyd, May 19 2020