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Lights Out On A Random Graph
Bradley Forrest, Nicole Manno
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We consider the generalized game Lights Out played on a graph and investigate the following question: for a given positive integer n, what is the probability that a graph chosen uniformly at random from the set of graphs with n vertices yields a universally solvable game of Lights Out? When n ≤11, we compute this probability exactly by determining if the game is universally solvable for each graph with n vertices. We approximate this probability for each positive integer n with n ≤100 by applying a Monte Carlo method using 1,000,000 trials. We also perform the analogous computations for connected graphs.
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