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Lights Out for
graphs related to one another by constructions
Laura E. Ballard, Erica L. Budge and Darin R. Stephenson
Vol. 12 (2019), No. 2, 181–201
DOI: 10.2140/involve.2019.12.181
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Abstract |
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The Lights Out problem on graphs, in which each vertex of the graph is in one of two states (“on” or “off”), has been investigated from a variety of perspectives over the last several decades, including parity domination, cellular automata, and harmonic functions on graphs. We consider a variant of the Lights Out problem in which the possible states for each vertex are indexed by the integers modulo . We examine the space of “null patterns” (i.e., harmonic functions) on graphs, and use this as a way to prove theorems about Lights Out on graphs that are related to one another by two main constructions. |
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Keywords
graph theory, Lights Out
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Mathematical Subject Classification 2010
Primary: 05C50, 05C69
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Milestones
Received: 15 December 2014
Revised: 6 September 2017
Accepted: 22 May 2018
Published: 8 October 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Laura E. Ballard | |
| Mathematics Department Syracuse University Syracuse, NY United States |
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| Erica L. Budge | |
| Department of Mathematics Hope College Holland, MI United States |
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| Darin R. Stephenson | |
| Department of Mathematics Hope College Holland, MI United States |
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