A123472 Number of weakly triangulated simple graphs on n unlabeled nodes.

1, 2, 4, 11, 33, 146, 886, 8483, 126029, 2866876, 95717334, 4534590984

Offset: 1

Author

N. J. A. Sloane, Oct 18 2006

Keywords

• nonn
• more

Comments

All weakly triangulated graphs are perfect.

Also known as weakly chordal graphs. This sequence counts both connected and disconnected graphs. - Jim Nastos, Jul 23 2025

Links

• S. Hougardy, Home Page
• S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.

Programs

Sage

for n in range(1, 11):
    count = 0
    for G in graphs(n):
        if G.is_weakly_chordal():
            count += 1
    print(n, count)
# Jim Nastos, Jul 25 2025

Formula

Euler transform of A079457. - Falk Hüffner, Jan 15 2016

Extensions

a(10) and a(11) added using formula by Falk Hüffner, Jan 15 2016

Name clarified by Jim Nastos, Jul 23 2025