A014377 Number of connected regular graphs of degree 7 with 2n nodes.

1, 0, 0, 0, 1, 5, 1547, 21609301, 733351105934, 42700033549946250, 4073194598236125132578, 613969628444792223002008202, 141515621596238755266884806115631

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard
• more

Examples

			a(0)=1 because the null graph (with no vertices) is vacuously 7-regular and connected.
		

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
• Eric Weisstein's World of Mathematics, Septic Graph

Crossrefs

Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)

7-regular simple graphs: this sequence (connected), A165877 (disconnected), A165628 (not necessarily connected).

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), this sequence (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).

Connected 7-regular simple graphs with girth at least g: this sequence (g=3), A181153 (g=4).

Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4), A184965 (g=5). (End)

Formula

a(n) = A184973(n) + A181153(n).

a(n) = A165628(n) - A165877(n).

This sequence is the inverse Euler transformation of A165628.

Extensions

Added another term from Meringer's page. Dmitry Kamenetsky, Jul 28 2009

Term a(8) (on Meringer's page) was found from running Meringer's GENREG for 325 processor days at U. Newcastle by Jason Kimberley, Oct 02 2009

a(9)-a(11) from Andrew Howroyd, Mar 13 2020

a(12) from Andrew Howroyd, May 19 2020