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A334443
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Number of unlabeled connected n-vertex graphs for which the lights out puzzle has a unique solution.
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1
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OFFSET
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1,4
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COMMENTS
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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.)
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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Inverse Euler transform of A334444.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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