A287009 -id:A287009 - cp's OEIS frontend

A198634 Number of weakly perfect graphs on n nodes.

1, 2, 4, 11, 33, 152, 1006, 11805, 257542, 11011758, 917095022, 145164791300

Offset: 1

Eric W. Weisstein, Feb 19 2013

A graph is weakly perfect if it has equal chromatic and clique numbers.

First differs from A287007 (fractional chromatic number equals chromatic number) at a(8). - Eric W. Weisstein, May 17 2017

Table of n, a(n) for n = 1..12
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 4361e42
Eric Weisstein's World of Mathematics, Weakly Perfect Graph

Cf. A287007, A287009, A287023.

a(n) = A287009(n) + A287023(n).

a(10) from Eric W. Weisstein, May 17 2017
a(11) added using tinygraph by Falk Hüffner, Aug 13 2017
a(12) added using tinygraph by Jakub Jablonski, Sep 26 2020

A287023 Number of simple disconnected weakly perfect graphs on n vertices.

Original entry on oeis.org

0, 1, 2, 5, 13, 43, 186, 1187, 13006, 270900, 11286208

Offset: 1

Eric W. Weisstein, May 18 2017

First differs from A287008 (number of simple disconnected graphs with equal chromatic and fractional chromatic number) at a(8).

Eric Weisstein's World of Mathematics, Disconnected Graph
Eric Weisstein's World of Mathematics, Weakly Perfect Graph

Cf. A198634 (number of not necessarily connected simple weakly perfect graphs).
Cf. A287009 (number of not connected simple weakly perfect graphs).
Cf. A287008 (number of simple disconnected graphs with equal chromatic and fractional chromatic number).

a(n) = A198634(n) - A287009(n).

a(11) from formula by Falk Hüffner, Aug 13 2017

cp's OEIS Frontend

A198634 Number of weakly perfect graphs on n nodes.

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