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2019 Lights Out for graphs related to one another by constructions
Laura E. Ballard, Erica L. Budge, Darin R. Stephenson
Involve 12(2): 181-201 (2019). DOI: 10.2140/involve.2019.12.181

Abstract

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 k. 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.

Citation

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Laura E. Ballard. Erica L. Budge. Darin R. Stephenson. "Lights Out for graphs related to one another by constructions." Involve 12 (2) 181 - 201, 2019. https://doi.org/10.2140/involve.2019.12.181

Information

Received: 15 December 2014; Revised: 6 September 2017; Accepted: 22 May 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06980497
MathSciNet: MR3864213
Digital Object Identifier: 10.2140/involve.2019.12.181

Subjects:
Primary: 05C50 , 05C69

Keywords: graph theory , Lights Out

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2019
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