A322555 - OEIS

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A322555

Number of labeled simple graphs on n vertices where all non-isolated vertices have the same degree.

1, 1, 2, 5, 18, 69, 390, 2703, 59474, 1548349, 168926258, 12165065351, 7074423247562, 2294426405580191, 4218009215702391954, 3810376434461484994317, 35102248193591661086921250, 156873334244228518638713087133, 4144940994226400702145709978234154

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

OFFSET

0,3

COMMENTS

Such graphs may be said to have regular support.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = 1 + Sum_{k=1..n} binomial(n, k)*(A295193(k) - 1). - Andrew Howroyd, Dec 17 2018

EXAMPLE

The a(4) = 18 edge sets:

{}

{{1,2},{3,4}}

{{1,3},{2,4}}

{{1,4},{2,3}}

{{1,2},{1,3},{2,3}}

{{1,2},{1,4},{2,4}}

{{1,3},{1,4},{3,4}}

{{2,3},{2,4},{3,4}}

{{1,2},{1,3},{2,4},{3,4}}

{{1,2},{1,4},{2,3},{3,4}}

{{1,3},{1,4},{2,3},{2,4}}

{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], SameQ@@Length/@Split[Sort[Join@@#]]&]], {n, 6}]

CROSSREFS

Cf. A000569, A005176, A038041, A059441, A295193, A306017, A306019, A319169, A320458.

Sequence in context: A363061 A288910 A249062 * A118814 A345878 A014271

Adjacent sequences: A322552 A322553 A322554 * A322556 A322557 A322558

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 15 2018

EXTENSIONS

a(8)-a(15) from Andrew Howroyd, Dec 17 2018

a(16)-a(18) from Andrew Howroyd, May 21 2020

STATUS

approved