A322659 - OEIS

A322659

Number of connected regular simple graphs on n labeled vertices.

1, 1, 1, 4, 13, 146, 826, 44808, 1074557, 155741296, 10381741786, 6939251270348, 2203360264480750, 4186526735251514044, 3747344007864300197810, 35041787059621536192399824, 156277111373298355107598128061, 4142122641757597729416733678931968

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

A graph is regular if all vertices have the same degree.

LINKS

Table of n, a(n) for n=1..18.

Gus Wiseman, The a(5) = 13 connected regular simple graphs.

Gus Wiseman, The a(6) = 146 connected regular simple graphs.

MATHEMATICA

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];

Table[If[n==1, 1, Length[Select[Subsets[Subsets[Range[n], {2}]], And[Union@@#==Range[n], SameQ@@Length/@Split[Sort[Join@@#]], Length[csm[#]]==1]&]]], {n, 6}]

CROSSREFS

Row sums of A324163.

Cf. A054921, A059441, A062740, A295193, A299353, A305078, A319190, A319612, A319729, A322635.

Sequence in context: A067634 A203215 A198159 * A042537 A220038 A132512

Adjacent sequences: A322656 A322657 A322658 * A322660 A322661 A322662

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 22 2018

EXTENSIONS

a(8)-a(15) from Andrew Howroyd, Dec 23 2018

a(16)-a(18) from Andrew Howroyd, Sep 02 2019

STATUS

approved