cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A198634 Number of weakly perfect graphs on n nodes.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Feb 19 2013

Keywords

Comments

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

Links

Crossrefs

Cf. A287007, A287009, A287023.

Formula

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

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, May 17 2017

Keywords

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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