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
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Apr 30 2020
STATUS
approved