A260813 Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 8.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 10, 101, 2510, 79605, 2607595, 81716416, 2472710752

Offset

0,19

Comments

The null graph on 0 vertices is vacuously connected, 3-regular, and bipartite; since it is acyclic, it has infinite girth.

Links

Table of n, a(n) for n=0..25.

G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.

G. Brinkmann, J. Goedgebeur and B.D. McKay, The Minimality of the Georges-Kelmans Graph, arXiv:2101.00943 [math.CO], 2021.

House of Graphs, Cubic bipartite graphs

Crossrefs

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Connected bipartite trivalent simple graphs with girth at least g: A006823 (g=4), A260811 (g=6), this sequence (g=8).

Sequence in context: A013268 A015487 A326428 * A062013 A023372 A025541

Adjacent sequences: A260810 A260811 A260812 * A260814 A260815 A260816

Keyword

nonn,more,hard

Author

Dylan Thurston, Jul 31 2015

Extensions

a(23)-a(24) from the House-of-Graphs added by R. J. Mathar, Sep 29 2017

a(25)-a(26) from Jan Goedgebeur, Aug 17 2021

Status

approved