A079571 Number of unlabeled, connected graphs on n vertices whose complements are bipartite.

1, 1, 1, 2, 5, 11, 32, 85, 299, 1115, 5474, 32298, 251129, 2527706, 33985846, 611846933, 14864650916, 488222721984, 21712049275189, 1308300679611460, 106897965189674281, 11852113048215107812, 1784730721403509209204, 365323537513403184463262

Offset: 0

Author

Jim Nastos, Jan 24 2003

Keywords

• nonn

Comments

Equivalently, number of bipartite graphs whose complement is connected. The only bipartite graphs with disconnected complement are complete bipartite graphs. - Falk Hüffner, Jan 22 2016

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A005142, A033995.

Programs

Mathematica

A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
b = etr[A005142[[# + 1]]&];
a[n_] := b[n] - Floor[n/2];
a /@ Range[0, 50] (* Jean-François Alcover, Sep 17 2019 *)

Formula

a(n) = A033995(n) - floor(n/2).

Extensions

Corrected and extended using formula by Falk Hüffner, Jan 22 2016

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 05 2018