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

0,5

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.

Links

Table of n, a(n) for n=0..19.

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].

Example

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

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).

Sequence in context: A290383 A099960 A324963 * A101182 A009207 A290878

Adjacent sequences: A218087 A218088 A218089 * A218091 A218092 A218093

Keyword

nonn,more

Author

Andy Hardt, Oct 20 2012

Status

approved