A014384 Number of connected regular graphs of degree 11 with 2n nodes.

1, 0, 0, 0, 0, 0, 1, 13, 8037796, 945095823831333, 187549729101764460261505, 66398444413512642732641312352088, 43100445012087185112567117500931916869587

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

Since the nontrivial 11-regular graph with the least number of vertices is K_12, there are no disconnected 11-regular graphs with less than 24 vertices. Thus for n<24 this sequence also gives the number of all 11-regular graphs on 2n vertices. - Jason Kimberley, Sep 25 2009

Examples

			The null graph on 0 vertices is vacuously connected and 11-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
• Eric Weisstein's World of Mathematics, Regular Graph

Crossrefs

11-regular simple graphs: this sequence (connected), A185213 (disconnected).

Connected regular simple graphs (with girth at least 3): 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), A014382 (k=10), this sequence (k=11).

Extensions

a(9)-a(10) from Andrew Howroyd, Mar 13 2020

a(11)-a(12) from Andrew Howroyd, May 19 2020