A165627 -id:A165627 - cp's OEIS frontend

A185163 Number of not necessarily connected 6-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7848, 367860, 21609300, 1470293675, 113314233804, 9799685588955

Offset: 0

Jason Kimberley, Mar 21 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), this sequence (k=6).

a(n) = A165627(n) - A185364(n).

a(n) = A184953(n) + A185053(n).

A339847 The number of labeled 6-regular graphs on n nodes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 1, 105, 30016, 11180820, 5188453830, 2977635137862, 2099132870973600, 1803595358964773088, 1872726690127181663775, 2329676580698022197516875, 3443086402825299720403673760, 5997229769947050271535917422040, 12218901113752712984458458475480428

Offset: 0

Atabey Kaygun, Dec 21 2020

nonn

Marni Mishna, Table of n, a(n) for n = 0..195 (terms 0..36 from Andrew Howroyd, terms 37..40 from Atabey Kaygun)
Frédéric Chyzak and Marni Mishna Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach, arXiv:2406.04753 [math.CO], 2024.
Atabey Kaygun, Counting Graphs with a Prescribed Degree Sequence.
Atabey Kaygun, Common LISP program that generates the sequence.
Atabey Kaygun, Enumerating Labeled Graphs that Realize a Fixed Degree Sequence, arXiv:2101.02299 [math.CO], 2021.
Marni Mishna, Maple code to generate terms.

Column k=6 of A059441.

Cf. A165627 (unlabeled case), A295193.

\\ Needs GraphsByDegreeSeq from links in A295193.
a(n)={my(M=GraphsByDegreeSeq(n, 6, (p,r)->6-valuation(p,x) <= r)); if(n>=7, vecsum(M[,2]), n==0)} \\ Andrew Howroyd, Dec 26 2020

Terms a(14) and beyond from Andrew Howroyd, Dec 26 2020

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A185163 Number of not necessarily connected 6-regular simple graphs on n vertices with girth exactly 3.

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A339847 The number of labeled 6-regular graphs on n nodes.

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