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

Author

Dylan Thurston, Jul 31 2015

Keywords

• nonn
• more
• hard

Comments

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

Links

• 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).

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