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Number of unlabeled point-determining bipartite graphs on n vertices.
3

%I #31 Apr 18 2021 20:41:16

%S 1,1,1,1,2,3,8,17,63,224,1248,8218,75992,906635,14447433,303100595,

%T 8415834690,309390830222,15105805368214,982300491033887

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

%C 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.

%H Ira Gessel and Ji Li, <a href="http://arxiv.org/abs/0705.0042">Enumeration of point-determining graphs</a>, arXiv:0705.0042 [math.CO]

%H Andy Hardt, Pete McNeely, Tung Phan, and Justin M. Troyka, <a href="http://arxiv.org/abs/1312.0542">Combinatorial species and graph enumeration</a>, arXiv:1312.0542 [math.CO].

%e 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

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

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

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

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

%K nonn,more

%O 0,5

%A _Andy Hardt_, Oct 20 2012