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

0,3

Comments

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

References

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

Links

Table of n, a(n) for n=0..14.

Example

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.

Crossrefs

Cf. A000088, A005176.

Sequence in context: A012936 A013091 A013168 * A013183 A049963 A368458

Adjacent sequences: A381583 A381584 A381585 * A381587 A381588 A381589

Keyword

nonn,more,new

Author

John P. McSorley, Feb 28 2025

Extensions

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

Status

approved