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A058862 Number of chordal labeled graphs (connected or not) with n nodes. 4
1, 2, 8, 61, 822, 18154, 617675, 30888596, 2192816760, 215488096587, 28791414081916, 5165908492061926, 1234777416771739141, 391374602835914994534, 164188178238479142509452 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. C. Wormald, Counting labeled chordal graphs. Graphs Combin. 1 (1985), no. 2, 193-200.

LINKS

Table of n, a(n) for n=1..15.

Jun Kawahara, Toshiki Saitoh, Hirofumi Suzuki, Ryo Yoshinaka, Enumerating All Subgraphs without Forbidden Induced Subgraphs via Multivalued Decision Diagrams, arXiv:1804.03822 [cs.DS], 2018.

FORMULA

From the relation G(x)=exp(g(x)) between generating functions for connected g(x) and all G(x) labeled structures and considering generating functions for chordal graphs (c_n, A007134), we have a(n) = c(n) + 1/n * Sum_{k=1}^(n - 1) k * binomial(n, k) * c(k) * a(n - k). [Formula edited by Michael De Vlieger, Jul 04 2018]

CROSSREFS

Cf. A007134.

Sequence in context: A188489 A085657 A005215 * A191482 A140722 A327078

Adjacent sequences:  A058859 A058860 A058861 * A058863 A058864 A058865

KEYWORD

nonn,nice,more

AUTHOR

Robert Castelo (rcastelo(AT)imim.es), Jan 06 2001

EXTENSIONS

a(13) from formula by Falk Hüffner, Jul 24 2019

a(14)-a(15) from Brendan McKay, Jun 05 2021

STATUS

approved

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Last modified October 23 10:17 EDT 2021. Contains 348211 sequences. (Running on oeis4.)