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2010 Lights Out on finite graphs
Stephanie Edwards, Victoria Elandt, Nicholas James, Kathryn Johnson, Zachary Mitchell, Darin Stephenson
Involve 3(1): 17-32 (2010). DOI: 10.2140/involve.2010.3.17


Lights Out is a one-player game played on a finite graph. In the standard game the vertices can be either on or off; pressing a vertex toggles its state and that of all adjacent vertices. The goal of the game is to turn off all of the lights. We study an extension of the game in which the state of a vertex may be one of a finite number of colors. We determine which graphs in certain families (spider graphs and generalized theta graphs) are winnable for every initial coloring. We also provide a construction that gives every always-winnable tree for any prime power number of colors.


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Stephanie Edwards. Victoria Elandt. Nicholas James. Kathryn Johnson. Zachary Mitchell. Darin Stephenson. "Lights Out on finite graphs." Involve 3 (1) 17 - 32, 2010.


Received: 13 April 2009; Revised: 21 December 2009; Accepted: 29 December 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1216.05086
MathSciNet: MR2672500
Digital Object Identifier: 10.2140/involve.2010.3.17

Primary: 05C15, 05C50, 05C78, 91A43

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.3 • No. 1 • 2010
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