A361254 Number of n-regular graphs on 2*n labeled nodes.

1, 1, 3, 70, 19355, 66462606, 2977635137862, 1803595358964773088, 15138592322753242235338875, 1793196665025885172290508971592750, 3040059281615704147007085764679679740691838, 74597015246986083384362428357508730776063716190667288, 26737694395324301026230134763403079891362936970900741153038680278

Offset: 0

Author

Atabey Kaygun, Mar 06 2023

Keywords

• nonn

Comments

These graphs share the same degree sequence as the complete bipartite graphs K(n,n).

Links

• Atabey Kaygun, Counting Graphs with a Prescribed Degree Sequence
• Atabey Kaygun, Enumerating Labeled Graphs that Realize a Fixed Degree Sequence, arXiv:2101.02299 [math.CO], 2021.

Crossrefs

Cf. A001223, A059441, A339987, A360437.

Programs

PARI

\\ See Links in A295193 for GraphsByDegreeSeq.
a(n)={if(n==0, 1, vecsum(GraphsByDegreeSeq(2*n, n, (p, r)->valuation(p,x) >= n-r)[, 2])) } \\ Andrew Howroyd, Mar 06 2023

Formula

a(n) = A059441(2*n, n).

Extensions

a(11)-a(12) from Andrew Howroyd, Mar 06 2023