A129586 Number of unlabeled connected bi-point-determining graphs (see A129583).

1, 0, 0, 1, 5, 31, 293, 4986, 151096, 8264613, 812528493, 144251345591, 46649058611515, 27744159658789435, 30603223477819571330, 63039669933956074333128, 243839768084859914114367906, 1779006737976575676931317142360, 24571827603944282248499044846893618

Offset: 1

Author

Ji Li (vieplivee(AT)hotmail.com), May 07 2007

Keywords

• nice
• nonn

Comments

The calculation of the number of connected bi-point-determining graphs is carried out by examining the connected components of bi-point-determining graphs. For more details, see linked paper "Enumeration of point-determining Graphs".

Links

• Martin Rubey, Table of n, a(n) for n = 1..29
• Florian Fürnsinn, Moritz Gangl, and Martin Rubey, Unexpectedly, a symmetry on unlabeled graphs, arXiv:2505.03665 [math.CO], 2025. See p. 18.
• Ira M. Gessel and Ji Li, Enumeration of point-determining Graphs, Journal of Combinatorial Theory, Series A 118 (2011) 591-612.

Crossrefs

Cf. graphs: labeled A006125, unlabeled A000568; connected graphs: labeled A001187, unlabeled A001349; point-determining graphs: labeled A006024, unlabeled A004110; connected point-determining graphs: labeled A092430, unlabeled A004108; connected co-point-determining graphs: labeled A079306, unlabeled A004108; bi-point-determining graphs: labeled A129583, unlabeled A129584; connected bi-point-determining graphs: labeled A129585, unlabeled A129586; phylogenetic trees: labeled A000311, unlabeled A000669.

Extensions

151096 and 8264613 from Vladeta Jovovic, May 10 2007

a(n) for n >= 11 from Martin Rubey, May 08 2025