%I
%S 1,0,1,1,7,21,234,2252,64420,2148355,183956671
%N Number of unlabeled mating graphs with n nodes and a degenerate adjacency matrix.
%C Mating graphs are graphs where no two nodes have the same set of neighbors.
%C Graphs with an invertible adjacency matrix are mating graphs.
%F a(n) = A004110(n)  A109717(n).
%t 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
%Y Cf. A004110, A109717.
%K nonn,more
%O 1,5
%A _Tanya Khovanova_, Aug 27 2008
%E a(8)a(11) by _Shreeyash Gotmare_, Aug 28 2017
