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A295193
Number of regular simple graphs on n labeled nodes.
33
1, 2, 2, 8, 14, 172, 932, 45936, 1084414, 155862512, 10382960972, 6939278572096, 2203360500122300, 4186526756621772344, 3747344008241368443820, 35041787059691023579970848, 156277111373303386104606663422, 4142122641757598618318165240180096
OFFSET
1,2
LINKS
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.
Sequence in context: A229730 A363181 A349648 * A248097 A098273 A342835
KEYWORD
nonn
AUTHOR
Álvar Ibeas, Nov 16 2017
EXTENSIONS
a(16)-a(18) from Andrew Howroyd, Aug 28 2019
STATUS
approved