A052433 Number of perfect connected undirected simple graphs on n nodes.

1, 1, 2, 6, 20, 105, 724, 7805, 126777, 3122221, 112392709, 5736233644, 404604893810

Offset

1,3

Comments

The triangle of the multiset transform (undirected simple graphs on n>=0 nodes with 0<=k<=n components) starts:

1

0 1

0 1 1

0 2 1 1

0 6 3 1 1

0 20 8 3 1 1

0 105 29 9 3 1 1

0 724 137 31 9 3 1 1

0 7805 890 146 32 9 3 1 1

0 126777 8859 926 148 32 9 3 1 1

0 3122221 136870 9043 935 149 32 9 3 1 1

0 112392709 3271052 138026 9079 937 149 32 9 3 1 1

0 5736233644 115835359 3281756 138215 9088 938 149 32 9 3 1 1

0 404604893810 5855863577 115988462 3282936 138251 9090 938 149 32 9 3 1 1 (R. J. Mathar, Mar 12 2018)

References

A. Brandstaedt, V. B. Le and J. P. Spinrad, Graph Classes: A Survey, SIAM Publications, 1999.

Links

Table of n, a(n) for n=1..13.

Adan Cabello, Lars Eirik Danielsen, Antonio J. Lopez-Tarrida, and Jose R. Portillo, Basic logical structures in quantum correlations, arXiv preprint arXiv:1211.5825 [quant-ph], 2012-2013.

Brendan McKay, Perfect graphs

Eric Weisstein's World of Mathematics, Perfect Graph

Formula

Inverse Euler transform of A052431.

Crossrefs

Sequence in context: A079457 A321911 A079455 * A078566 A076323 A241782

Adjacent sequences: A052430 A052431 A052432 * A052434 A052435 A052436

Keyword

nonn,hard,more

Author

Eric W. Weisstein

Extensions

More terms from Vladeta Jovovic, Jul 29 2003

a(12) using A052431 by Falk Hüffner, Jan 15 2016

a(13) using Brendan McKay's A052431(13) by Alois P. Heinz, Mar 11 2018

Status

approved