A014381 Number of connected regular graphs of degree 9 with 2n nodes.

1, 0, 0, 0, 0, 1, 9, 88193, 113314233813, 281341168330848874, 1251392240942040452186674, 9854603833337765095207342173991, 134283276101750327256393048776114352985

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more
• hard

Comments

Since the nontrivial 9-regular graph with the least number of vertices is K_10, there are no disconnected 9-regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9-regular graphs on 2n vertices. - Jason Kimberley, Sep 25 2009

Examples

			The null graph on 0 vertices is vacuously connected and 9-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

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), this sequence (k=9), A014382 (k=10), A014384 (k=11).

9-regular simple graphs: this sequence (connected), A185293 (disconnected).

Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).

Connected 9-regular simple graphs with girth exactly g: A184993 (g=3).

Formula

a(n) = A184993(n) + A181170(n).

Extensions

a(8) appended using the symmetry of A051031 by Jason Kimberley, Sep 25 2009

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

a(10) corrected and a(11)-a(12) from Andrew Howroyd, May 19 2020