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

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

Offset

1,3

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

Table of n, a(n) for n=1..11.

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

Formula

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

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).

Sequence in context: A076323 A241782 A268562 * A243252 A366760 A136795

Adjacent sequences: A287006 A287007 A287008 * A287010 A287011 A287012

Keyword

nonn,more

Author

Eric W. Weisstein, May 17 2017

Extensions

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

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

Status

approved