A126750 Number of 2-connected (or biconnected) graphs on n nodes with chromatic number 2.

0, 0, 0, 1, 1, 5, 8, 42, 146, 956, 6643, 65921, 818448, 13442572, 287665498, 8099980771, 300760170216, 14791653463768, 967055338887805, 84368806391412395, 9855854129239183783, 1546801291978378704267

Offset

1,6

Comments

Equally, number of 2-connected (or biconnected) bipartite graphs on n nodes.

Also number of biconnected triangle-free graphs on n nodes with chromatic number 2, since chromatic number 2 implies triangle-free. - Gordon Royle, Apr 11 2007

See the Gainer-Dewar/Gessel reference for formulas and Sage code. - Ralf Stephan, May 18 2013

Links

Table of n, a(n) for n=1..22.

Keith M. Briggs, Combinatorial Graph Theory

C. J. Colbourn and C. Huybrechts, Fully gated graphs,: recognition and convex operations, Discrete Math., 308 (2008), 5184-5195.

A. Gainer-Dewar and I. M. Gessel, Enumeration of bipartite graphs and bipartite blocks, arXiv:1304.0139 [math.CO], 2013-2014.

Crossrefs

A diagonal of triangle in A126749.

Sequence in context: A073930 A342021 A130223 * A256401 A109292 A275571

Adjacent sequences: A126747 A126748 A126749 * A126751 A126752 A126753

Keyword

nonn

Author

N. J. A. Sloane, Feb 18 2007, Oct 01 2008

Status

approved