A140981
Number of graphs with n vertices that have an even determinant for the adjacency matrix.
Original entry on oeis.org
1, 1, 4, 7, 34, 109, 1044, 8303, 274668, 7451736, 1018997864
Offset: 1
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
A334444
Number of unlabeled n-vertex graphs for which the lights out puzzle has a unique solution.
Original entry on oeis.org
1, 1, 2, 4, 13, 47, 339, 4043, 98375, 4553432, 403286335
Offset: 1
- Bradley Forrest and Nicole Manno, Lights Out on a Random Graph, The PUMP Journal of Undergraduate Research, 5 (2022), 165-175; arXiv:2108.07349 [math.CO], 2021-2022. See Table 1.
- I. Short (ed.) and Andrey Zabolotskiy (auth.), Problem 92.2, Irish Math. Soc. Bulletin, 92 (2023), p. 68; see also J. P. McCarthy (ed.) and the North Kildare Mathematics Problem Club (auth.), Solution 92.2, Irish Math. Soc. Bulletin, 94 (2024), p. 101. This essentially proves that A141040 is a bisection.
- Eric Weisstein's World of Mathematics, Lights Out Puzzle
Showing 1-3 of 3 results.