A331014 -id:A331014 - cp's OEIS frontend

A331013 Number of unlabeled bicolored bipartite graphs on 2n nodes having n nodes of each color with no edges between vertices of the same color and edges having two colors and allowing the node color classes to be interchanged. Edge colors are swappable (permuted by the symmetric group).

1, 4, 13, 104, 1507, 64203, 8426875, 3671999389, 5366787092478, 26433809041087192, 441089058039611200394, 25113998661290096278734134, 4918524299370332513672165781112, 3340919807757080784843712707230030713, 7933888983010307508332924524920878232000997, 66370395190630232518212377765981306426650525779505

Offset: 1

Marko Riedel, Jan 06 2020

nonn

Color swaps of the node colors are reflections of the biclique about a vertical axis, with one part on the left and the other on the right. Edge colors are distinct from the two node colors.

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

Marko Riedel, Math.StackExchange, Counting bicliques
Marko Riedel, Cycle indices for K_{n,n} including shuffles and reflections as well as Power Group Enumeration implementation.

Cf. A007139, A331014.

cp's OEIS Frontend

A331013 Number of unlabeled bicolored bipartite graphs on 2n nodes having n nodes of each color with no edges between vertices of the same color and edges having two colors and allowing the node color classes to be interchanged. Edge colors are swappable (permuted by the symmetric group).

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