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Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 6.
1

%I #20 Jun 03 2023 12:02:04

%S 1,0,0,0,0,0,0,1,1,3,10,28,162,1201,11415,125571,1514489

%N Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 6.

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

%H G. Brinkmann, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199610)23:2&lt;139::AID-JGT5&gt;3.0.CO;2-U">Fast generation of cubic graphs</a>, Journal of Graph Theory, 23(2):139-149, 1996.

%H House of Graphs, <a href="https://houseofgraphs.org/meta-directory/cubic#cubic_bipartite">Cubic bipartite graphs</a>

%Y 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).

%Y Connected bipartite trivalent simple graphs with girth at least g: A006823 (g=4), this sequence (g=6), A260813 (g=8).

%K nonn,more,hard

%O 0,10

%A _Dylan Thurston_, Jul 31 2015