

A079565


Number of unlabeled and connected graphs on n vertices which are either bipartite or cobipartite.


0



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

1,3


COMMENTS

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 cobipartite.  Falk Hüffner, Jan 22 2016


LINKS

Table of n, a(n) for n=1..20.


FORMULA

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


EXAMPLE

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.


CROSSREFS

Sequence in context: A214843 A151528 A132803 * A052890 A052814 A192401
Adjacent sequences: A079562 A079563 A079564 * A079566 A079567 A079568


KEYWORD

more,nonn


AUTHOR

Jim Nastos, Jan 24 2003


EXTENSIONS

More terms using formula by Falk Hüffner, Jan 22 2016


STATUS

approved



