A103869 Number of unlabeled graphs with n nodes whose adjacency matrix has nonzero even determinant.

0, 0, 1, 0, 9, 10, 354, 1752, 141494, 3313095, 728952205

Offset: 1

Author

Tanya Khovanova, Aug 29 2008

Keywords

• more
• nonn

Crossrefs

Cf. A133206, A140981, A141040, A109717, A000088.

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 && Mod[Det[ToAdjacencyMatrix[lg[[ # ]]]], 2] == 0 &]]]]; k

Formula

a(n) = A140981(n) - A133206(n).

For odd n, a(n) = A109717(n). For even n, a(n) = A109717(n) - A141040(n/2). - Max Alekseyev, Feb 20 2024

Extensions

a(8)-a(10) from Andrew Howroyd, Nov 04 2017

a(11) from A109717 added by Max Alekseyev, Feb 20 2024