A381586 Number of simple graphs on n unlabeled vertices whose degree sequence is consecutive.

1, 1, 2, 4, 9, 24, 98, 622, 7293, 162052, 6997100, 578605618, 90558592724, 26673271109299, 14758661765740616

Offset: 0

Author

John P. McSorley, Feb 28 2025

Keywords

• nonn
• more

Comments

A graph has a consecutive degree sequence if its distinct degrees are consecutive integers. This includes all regular graphs.

Examples

			For n = 4 there are 11 non-isomorphic graphs G on 4 vertices. An example with consecutive degree sequence is 4K_1, with degree sequence 0000; and an example with non-consecutive degree sequence is K_1 U K_3 with degree sequence 0222. The only other G with non-consecutive degree sequence is K_{1,3} with degree sequence 1113. Thus a(4) = 9.
		

References

• R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).

Crossrefs

Cf. A000088, A005176.

Extensions

a(8)-a(14) from Andrew Howroyd, Feb 28 2025