A079457 Number of unlabeled and connected graphs which are weakly chordal. (G is weakly chordal iff there are no induced cycles of size 5 or more in G nor in its complement.)

1, 1, 2, 6, 20, 103, 706, 7423, 116476, 2730992, 92711668, 4435835227

Offset: 1

Author

Jim Nastos, Jan 13 2003

Keywords

• more
• nonn

Comments

Also known as the "weakly triangulated" graphs. Contains the chordal and cochordal graphs and is contained in the class of Perfect graphs.

Links

• R. Hayward, Weakly triangulated graphs, Journal Comb. Theory (Series B) 39 (1985) 200-208.
• R. Hayward, Generating Weakly Triangulated Graphs, Journal of Graph Theory 21 (1996) 67-69.
• R. Hayward, J. Spinrad, R. Sritharan, Weakly Chordal Graph Algorithms via Handles, Proc. 11th SODA (2000) 42-49.
• F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 26b03c7

Formula

Inverse Euler transform of A123472.

Extensions

a(10)-a(12) added using tinygraph by Falk Hüffner, Jan 15 2016