A399264 - OEIS

A399264

Number of asymmetric connected bipartite graphs with n vertices.

1, 0, 0, 0, 0, 0, 3, 8, 74, 478, 4576, 49134, 682541, 11868102, 265639155

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OFFSET

1,7

COMMENTS

For n >= 2, a connected bipartite graph has a unique bipartition, up to interchanging the two parts. For equal part sizes, automorphisms interchanging the two parts must also be excluded.

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York, 1973.

V. Jovovic, Symmetry Types of Combinatorial Structures, manuscript, 2026.

LINKS

Table of n, a(n) for n=1..15.

Vladeta Jovovic, Computation of Asymmetric Connected Bipartite Graphs

Vladeta Jovovic, Illustrations of Asymmetric Connected Bipartite Graphs

FORMULA

Let b(p,q) be the number of connected asymmetric bipartite graphs with bipartition sizes p and q, counted up to isomorphism. Then a(n) = Sum_{1 <= p <= q, p+q=n} b(p,q).

EXAMPLE

a(7) = 3: there are 3 nonisomorphic connected bipartite graphs on 7 vertices with trivial automorphism group.

CROSSREFS

Cf. A005142 (connected bipartite graphs), A124059 (connected asymmetric graphs).

Sequence in context: A095051 A362990 A092372 * A396634 A208817 A356529

Adjacent sequences: A399250 A399260 A399261 * A399266 A399267 A399268

KEYWORD

nonn,hard,more,new

AUTHOR

Vladeta Jovovic, Aug 25 2026

STATUS

approved