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A123467 Number of trivially-perfect graphs on n nodes. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..29.

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.

FORMULA

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

CROSSREFS

Cf. A000081.

Sequence in context: A292556 A145550 A000081 * A124497 A286983 A289971

Adjacent sequences:  A123464 A123465 A123466 * A123468 A123469 A123470

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 18 2006

STATUS

approved

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Last modified December 10 20:46 EST 2017. Contains 295855 sequences.