A218090 Number of unlabeled point-determining bipartite graphs on n vertices.

1, 1, 1, 1, 2, 3, 8, 17, 63, 224, 1248, 8218, 75992, 906635, 14447433, 303100595, 8415834690, 309390830222, 15105805368214, 982300491033887

Offset: 0

Author

Andy Hardt, Oct 20 2012

Keywords

• nonn
• more

Comments

A graph is point-determining if no two vertices have the same set of neighbors. This kind of graph is also called a mating graph.

Examples

			Consider n = 3. The triangle graph is point-determining, but it is not bipartite, so it is not counted in a(3). The graph *--*--* is bipartite, but it is not point-determining (the vertices on the two ends have the same neighborhood), so it is also not counted in a(3). The only graph counted in a(3) is the graph *--*  *. - _Justin M. Troyka_, Nov 27 2013
		

Links

• Ira Gessel and Ji Li, Enumeration of point-determining graphs, arXiv:0705.0042 [math.CO]
• Andy Hardt, Pete McNeely, Tung Phan, and Justin M. Troyka, Combinatorial species and graph enumeration, arXiv:1312.0542 [math.CO].

Crossrefs

Cf. A006024, A004110 (labeled and unlabeled point-determining graphs).

Cf. A092430, A004108 (labeled and unlabeled connected point-determining graphs).

Cf. A232699 (labeled point-determining bipartite graphs).

Cf. A232700, A088974 (labeled and unlabeled connected point-determining bipartite graphs).