A287009 Number of connected simple weakly perfect graphs on n vertices.

1, 1, 2, 6, 20, 109, 820, 10618, 244536, 10740858, 905808814

Offset: 1

Author

Eric W. Weisstein, May 17 2017

Keywords

• nonn
• more

Comments

First differs from A243252 (connected simple graphs whose fractional number equals its chromatic number) at a(8). The three (connected) 8-node graphs that have equal chromatic and fractional chromatic numbers but are not weakly perfect are the 4-antiprism graph and 50- and 84-Johnson solid skeleton graphs, all of which have clique number 3 but chromatic and fractional chromatic number 4.

Links

• F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 4361e42
• Eric Weisstein's World of Mathematics, Connected Graph
• Eric Weisstein's World of Mathematics, Weakly Perfect Graph

Crossrefs

Cf. A198634 (not necessarily connected weakly perfect simple graphs on n nodes).

Cf. A287023 (disconnected weakly perfect simple graphs on n nodes).

Cf. A243252 (connected simple graphs whose fractional number equals its chromatic number).

Formula

a(n) = A198634(n) - A287023(n).

Extensions

a(9)-a(10) from Eric W. Weisstein, May 18 2017

a(11) added using tinygraph by Falk Hüffner, Aug 13 2017