A129584 - OEIS

A129584

Number of unlabeled bi-point-determining graphs: graphs in which no two vertices have the same neighborhoods or the same augmented neighborhoods (the augmented neighborhood of a vertex is the neighborhood of the vertex union the vertex itself).

%I #10 Feb 23 2019 14:52:09

%S 1,0,0,1,6,36,324,5280,156088,8415760

%N Number of unlabeled bi-point-determining graphs: graphs in which no two vertices have the same neighborhoods or the same augmented neighborhoods (the augmented neighborhood of a vertex is the neighborhood of the vertex union the vertex itself).

%C This is the unlabeled case of bi-point-determining graphs, which are basically graphs that are both point-determining (no two vertices have the same neighborhoods) and co-point-determining (graphs whose complements are point-determining)

%H Ira M. Gessel and Ji Li, <a href="https://doi.org/10.1016/j.jcta.2010.03.009">Enumeration of point-determining Graphs</a>, Journal of Combinatorial Theory, Series A 118 (2011) 591-612.

%Y 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.

%K nice,nonn,more

%O 1,5

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