A381586 - OEIS

%I #19 Mar 07 2025 08:16:32

%S 1,1,2,4,9,24,98,622,7293,162052,6997100,578605618,90558592724,

%T 26673271109299,14758661765740616

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

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

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

%e 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.

%Y Cf. A000088, A005176.

%K nonn,more,new

%O 0,3

%A _John P. McSorley_, Feb 28 2025

%E a(8)-a(14) from _Andrew Howroyd_, Feb 28 2025