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An iterative
strategy for Lights Out on Petersen graphs
Bruce Torrence and Robert Torrence
Vol. 9 (2016), No. 5, 721–732
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Abstract |
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We establish some preliminary results for Sutner’s game, known as Lights Out, played on the generalized Petersen graph . While all regular Petersen graphs admit game configurations that are not solvable, we prove that every game on the graph has a unique solution. Moreover, we introduce a simple iterative strategy for finding the solution to any game on , and generalize its application to a wider class of graphs. |
Keywords
Lights Out, Petersen graph, game, sigma plus game
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Mathematical Subject Classification 2010
Primary: 05C50, 37B99, 90C27, 91A43, 05C57
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Milestones
Received: 30 August 2013
Revised: 25 May 2015
Accepted: 6 November 2015
Published: 25 August 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Bruce Torrence | |
| Department of Mathematics Randolph–Macon College P.O. Box 5005 Ashland, VA 23005 United States |
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| Robert Torrence | |
| Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, VA 24061 United States |
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