A079571 -id:A079571 - cp's OEIS frontend

A079565 Number of unlabeled and connected graphs on n vertices which are either bipartite or co-bipartite.

1, 1, 2, 6, 16, 49, 129, 481, 1845, 9506, 57896, 463909, 4769436, 65179170, 1187099045, 29082860878, 960963147303, 42920936851975, 2594399793419459, 212465886865393053, 23596018831885668391, 3557502387712889568013, 728850489548729072323085

Offset: 1

Jim Nastos, Jan 24 2003

nonn

G is bipartite iff the vertices can be partitioned into two sets such that all the edges in the graph go from one of these sets to the other. G is cobipartite iff the complement of G is bipartite.

For n >= 5, no graph can be both bipartite and co-bipartite. - Falk Hüffner, Jan 22 2016

			Let G be a graph with 5 vertices, 4 of which form a path and the 5th adjacent only to the two vertices in the middle of the path. Then G is not bipartite nor cobipartite because there is a triangle in both G and its complement.

Andrew Howroyd, Table of n, a(n) for n = 1..50

Cf. A005142, A079571.

A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
A033995 = Import["https://oeis.org/A033995/b033995.txt", "Table"][[All, 2]];
a[n_] := If[n<5, {1, 1, 2, 6}[[n]], A005142[[n+1]] + A033995[[n+1]] - Floor[n/2]];
a /@ Range[1, 50] (* Jean-François Alcover, Sep 17 2019 *)

For n >= 5, a(n) = A079571(n) + A005142(n). - Falk Hüffner, Jan 22 2016

More terms using formula by Falk Hüffner, Jan 22 2016

Terms a(21) and beyond from Andrew Howroyd, Sep 05 2018

cp's OEIS Frontend

A079565 Number of unlabeled and connected graphs on n vertices which are either bipartite or co-bipartite.

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