A103869
Number of unlabeled graphs with n nodes whose adjacency matrix has nonzero even determinant.
Original entry on oeis.org
0, 0, 1, 0, 9, 10, 354, 1752, 141494, 3313095, 728952205
Offset: 1
-
k = {}; For[i = 1, i < 8, i++, lg = ListGraphs[i] ; len = Length[lg]; k = Append[k, Length[Select[Range[len], Det[ToAdjacencyMatrix[lg[[ # ]]]] != 0 && Mod[Det[ToAdjacencyMatrix[lg[[ # ]]]], 2] == 0 &]]]]; k
A133206
Number of unlabeled graphs with n nodes and a degenerate adjacency matrix.
Original entry on oeis.org
1, 1, 3, 7, 25, 99, 690, 6551, 133174, 4138641, 290045659
Offset: 1
-
k = {}; For[i = 1, i < 8, i++, lg = ListGraphs[i] ; len = Length[lg]; k = Append[k, Length[Select[Range[len], Det[ToAdjacencyMatrix[lg[[ # ]]]] == 0 &]]]]; k
A133279
Number of unlabeled mating graphs with n nodes and a degenerate adjacency matrix.
Original entry on oeis.org
1, 0, 1, 1, 7, 21, 234, 2252, 64420, 2148355, 183956671
Offset: 1
-
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
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