Lights Out on Petersen Graphs
Bruce F. Torrence, Robert Torrence · 2013
We establish some preliminary results for Sutner’s + game, i.e. \Lights Out, played on the generalized Petersen graph P (n;k). While all regular Petersen graphs admit game congurations that are not solvable, we prove that every game on the P (2n;n) graph has a unique solution. Moreover, we introduce an exceedingly simple strategy for nding the solution to any game on these graphs. Surprisingly, this same strategy is shown to work on a few other Petersen graphs, and on some other related graphs.