A295193 Number of regular simple graphs on n labeled nodes.

1, 2, 2, 8, 14, 172, 932, 45936, 1084414, 155862512, 10382960972, 6939278572096, 2203360500122300, 4186526756621772344, 3747344008241368443820, 35041787059691023579970848, 156277111373303386104606663422, 4142122641757598618318165240180096

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..24

E. A. Bender and E. R. Canfield, The asymptotic number of labeled graphs with given degree sequences, Journal of Combinatorial Theory, Series A, 24 (1978), 296-307.

Andrew Howroyd, PARI Program

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

B. D. McKay, Applications of a technique for labelled enumeration, Congress. Numerantium, 40 (1983), 207-221.

Wikipedia, Regular graph

Example

From Gus Wiseman, Dec 19 2018: (Start)
A graph is regular if all vertices have the same degree. For example, the a(4) = 8 simple regular graphs are:
  1 2
  3 4
.
  4---1  3---1  2---1
  3---2  4---2  4---3
.
  3---4  4---3  4---2
  |   |  |   |  |   |
  1---2  1---2  1---3
.
  4---3
  | X |
  2---1
(End)

Mathematica

Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {2}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {k, 0, n-1}], {n, 1, 9}] (* Gus Wiseman, Dec 19 2018 *)

Prog

(PARI) \\ See link for program file.
for(n=1, 10, print1(A295193(n), ", ")) \\ Andrew Howroyd, Aug 28 2019

Crossrefs

Row sums of A059441.

Cf. A005176 (unlabeled equivalent), A058891, A116539, A299353, A306017, A306021, A319189, A319190, A319612, A319729.

Sequence in context: A229730 A363181 A349648 * A248097 A098273 A342835

Adjacent sequences: A295190 A295191 A295192 * A295194 A295195 A295196

Keyword

nonn

Author

Álvar Ibeas, Nov 16 2017

Extensions

a(16)-a(18) from Andrew Howroyd, Aug 28 2019

Status

approved