A088974 Number of (nonisomorphic) connected bipartite graphs with minimum degree at least 2 and with n vertices.

0, 0, 0, 1, 1, 5, 9, 45, 160, 1018, 6956, 67704, 830392, 13539344, 288643968, 8112651795, 300974046019, 14796399706863, 967194378235406, 84374194347669628, 9856131011755992817, 1546820212559671605395

Offset

1,6

Comments

The terms were computed using the program Nauty.

As shown in the Hardt et al. reference, this sequence (for n >= 3) also enumerates the connected point-determining bipartite graphs. - Justin M. Troyka, Nov 27 2013

Links

Table of n, a(n) for n=1..22.

Brendan McKay, Nauty

Andy Hardt, Pete McNeely, Tung Phan, and Justin M. Troyka, Combinatorial species and graph enumeration, arXiv:1312.0542 [math.CO].

Example

Consider n = 4.  There is one connected bipartite graph with minimum degree at least 2: the square graph.  Also there is one connected point-determining bipartite graph: the graph *--*--*--*. - Justin M. Troyka, Nov 27 2013

Crossrefs

Cf. A006024, A004110 (labeled and unlabeled point-determining graphs [the latter is also unlabeled graphs w/ min. degree >= 2]).

Cf. A059167 (labeled graphs w/ min. degree >= 2).

Cf. A092430, A004108 (labeled and unlabeled connected point-determining graphs [the latter is also unlabeled connected graphs w/ min. degree >= 2]).

Cf. A059166 (labeled connected graphs w/ min. degree >= 2).

Cf. A232699, A218090 (labeled and unlabeled point-determining bipartite graphs).

Cf. A232700 (labeled connected point-determining bipartite graphs).

Sequence in context: A149501 A149502 A219701 * A105182 A100457 A080872

Adjacent sequences: A088971 A088972 A088973 * A088975 A088976 A088977

Keyword

nonn

Author

Felix Goldberg (felixg(AT)tx.technion.ac.il), Oct 30 2003

Extensions

More terms from Andy Hardt, Oct 31 2012

Status

approved