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A334443
Number of unlabeled connected n-vertex graphs for which the lights out puzzle has a unique solution.
1
1, 0, 1, 2, 9, 33, 290, 3692, 94280, 4454654
OFFSET
1,4
COMMENTS
The lights out puzzle on a graph has a unique solution if and only if the graph has an odd number of matchings. (See Section 6 in the paper by Eriksson, Eriksson, and Sjöstrand.)
LINKS
H. Eriksson, K. Eriksson, J. Sjöstrand, Note on the lamp lighting problem, Advances in Applied Mathematics 27 (2001), 357-366.
Eric Weisstein's World of Mathematics, Lights Out Puzzle
EXAMPLE
The connected 4-vertex graphs for which the lights out puzzle has a unique solution are the path and the cycle, so a(4)=2.
CROSSREFS
Cf. A076436.
Inverse Euler transform of A334444.
Sequence in context: A150936 A109719 A263685 * A301868 A288958 A212348
KEYWORD
nonn,more
AUTHOR
STATUS
approved