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

1,5

Comments

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

Graphs with an invertible adjacency matrix are mating graphs.

Links

Table of n, a(n) for n=1..11.

Formula

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

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

Crossrefs

Cf. A004110, A109717.

Sequence in context: A060146 A357673 A111878 * A192734 A220161 A213152

Adjacent sequences: A133276 A133277 A133278 * A133280 A133281 A133282

Keyword

nonn,more

Author

Tanya Khovanova, Aug 27 2008

Extensions

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

Status

approved