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
Keywords
Examples
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)
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
Crossrefs
Programs
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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 *) -
PARI
\\ See link for program file. for(n=1, 10, print1(A295193(n), ", ")) \\ Andrew Howroyd, Aug 28 2019
Extensions
a(16)-a(18) from Andrew Howroyd, Aug 28 2019