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A287009
Number of connected simple weakly perfect graphs on n vertices.
2
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
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
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