A339987 -id:A339987 - cp's OEIS frontend

A360437 The number of labeled graphs on n nodes whose degree sequences realize the first n even terms of A001223 (the prime gap sequence).

0, 0, 0, 0, 1, 13, 126, 288, 8160, 110800, 8552205, 253822863, 21802799690, 1751958608840, 231900341949104, 8821242453833942, 1943505339202134370, 417503287597170065730, 18004075657522393347770, 7276527497090264178405240, 2096206309349359523650043220

Offset: 1

Atabey Kaygun, Feb 07 2023

nonn

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.

Cf. A001223, A339987.

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

Original entry on oeis.org

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

Offset: 0

Atabey Kaygun, Mar 06 2023

nonn

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

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.

Cf. A001223, A059441, A339987, A360437.

\\ 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

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

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

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A360437 The number of labeled graphs on n nodes whose degree sequences realize the first n even terms of A001223 (the prime gap sequence).

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

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