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%I #16 Aug 13 2017 13:15:05
%S 1,1,2,6,20,109,820,10618,244536,10740858,905808814
%N Number of connected simple weakly perfect graphs on n vertices.
%C 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.
%H F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 4361e42
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WeaklyPerfectGraph.html">Weakly Perfect Graph</a>
%F a(n) = A198634(n) - A287023(n).
%Y Cf. A198634 (not necessarily connected weakly perfect simple graphs on n nodes).
%Y Cf. A287023 (disconnected weakly perfect simple graphs on n nodes).
%Y Cf. A243252 (connected simple graphs whose fractional number equals its chromatic number).
%K nonn,more
%O 1,3
%A _Eric W. Weisstein_, May 17 2017
%E a(9)-a(10) from _Eric W. Weisstein_, May 18 2017
%E a(11) added using tinygraph by _Falk Hüffner_, Aug 13 2017