A052433 - OEIS

%I #30 Jan 13 2024 11:51:16

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

%T 404604893810

%N Number of perfect connected undirected simple graphs on n nodes.

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

%C 1

%C 0 1

%C 0 1 1

%C 0 2 1 1

%C 0 6 3 1 1

%C 0 20 8 3 1 1

%C 0 105 29 9 3 1 1

%C 0 724 137 31 9 3 1 1

%C 0 7805 890 146 32 9 3 1 1

%C 0 126777 8859 926 148 32 9 3 1 1

%C 0 3122221 136870 9043 935 149 32 9 3 1 1

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

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

%C 0 404604893810 5855863577 115988462 3282936 138251 9090 938 149 32 9 3 1 1 (_R. J. Mathar_, Mar 12 2018)

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

%H Adan Cabello, Lars Eirik Danielsen, Antonio J. Lopez-Tarrida, and Jose R. Portillo, <a href="http://arxiv.org/abs/1211.5825">Basic logical structures in quantum correlations</a>, arXiv preprint arXiv:1211.5825 [quant-ph], 2012-2013.

%H Brendan McKay, <a href="http://dcsmail.anu.edu.au/pipermail/nauty-list/2002/000031.html">Perfect graphs</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectGraph.html">Perfect Graph</a>

%F Inverse Euler transform of A052431.

%K nonn,hard,more

%O 1,3

%A _Eric W. Weisstein_

%E More terms from _Vladeta Jovovic_, Jul 29 2003

%E a(12) using A052431 by _Falk Hüffner_, Jan 15 2016

%E a(13) using _Brendan McKay_'s A052431(13) by _Alois P. Heinz_, Mar 11 2018