A133279 Number of unlabeled mating graphs with n nodes and a degenerate adjacency matrix.

1, 0, 1, 1, 7, 21, 234, 2252, 64420, 2148355, 183956671

Offset: 1

Author

Tanya Khovanova, Aug 27 2008

Keywords

• nonn
• more

Comments

Mating graphs are graphs where no two nodes have the same set of neighbors.

Graphs with an invertible adjacency matrix are mating graphs.

Crossrefs

Cf. A004110, A109717.

Programs

Mathematica

k = {}; For[i = 1, i < 8, i++, lg = ListGraphs[i] ; len = Length[lg]; k = Append[k, Length[Select[Range[len], Det[ToAdjacencyMatrix[lg[[ # ]]]] == 0 && Length[Union[ToAdjacencyMatrix[lg[[ # ]]]]] == i &]]]]; k

Formula

a(n) = A004110(n) - A109717(n).

Extensions

a(8)-a(11) by Shreeyash Gotmare, Aug 28 2017