Vol. 9, No. 5, 2016

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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

We establish some preliminary results for Sutner’s σ+ game, known as Lights Out, played on the generalized Petersen graph P(n,k). While all regular Petersen graphs admit game configurations that are not solvable, we prove that every game on the P(2n,n) graph has a unique solution. Moreover, we introduce a simple iterative strategy for finding the solution to any game on P(2n,n), and generalize its application to a wider class of graphs.

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Lights Out, Petersen graph, game, sigma plus game
Mathematical Subject Classification 2010
Primary: 05C50, 37B99, 90C27, 91A43, 05C57
Received: 30 August 2013
Revised: 25 May 2015
Accepted: 6 November 2015
Published: 25 August 2016

Communicated by Kenneth S. Berenhaut
Bruce Torrence
Department of Mathematics
Randolph–Macon College
P.O. Box 5005
Ashland, VA 23005
United States
Robert Torrence
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
United States