A123467 Number of trivially-perfect graphs on n nodes.

1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12486, 32973, 87811, 235381, 634847, 1721159, 4688676, 12826228, 35221832, 97055181, 268282855, 743724984, 2067174645, 5759636510, 16083734329, 45007066269, 126186554308, 354426847597

Offset: 1

Author

N. J. A. Sloane, Oct 18 2006

Keywords

• nonn

Comments

Is this the same as A000081 with a different offset? - N. J. A. Sloane

Yes, because it equals the number of rooted forests with n nodes (see Golumbic reference). The Euler transform shifts this sequence by one. Thus the number of connected trivially-perfect graphs on n nodes is a(n-1). - Falk Hüffner, Nov 26 2015

Links

• M. C. Golumbic, Trivially perfect graphs, Discr. Math. 24(1) (1978), 105-107.
• S. Hougardy, Home Page
• S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.

Crossrefs

Cf. A000081.

Formula

a(n) = A000081(n+1) - Falk Hüffner, Nov 26 2015