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A
group-labeling version of the Lights Out game
Darren B. Parker and Vasily Zadorozhnyy
Vol. 14 (2021), No. 4, 541–554
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Abstract |
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The Lights Out game, originally an electronic game played on a grid, is a solitaire game that can be played on any simple graph. It has been generalized to be played with multiple on-states, where each vertex state is represented by a label in . We define a new variant of the Lights Out game, where the vertex labels can come from any group . This new game depends deeply on the group structure of and gives us a significantly different game for cyclic groups. We investigate problems related to counting winnable labelings in the case . |
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Keywords
Lights Out, vertex labeling, games on graphs
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Mathematical Subject Classification 2010
Primary: 05C20, 06B99
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Milestones
Received: 6 November 2017
Revised: 19 June 2018
Accepted: 19 June 2020
Published: 23 October 2021
Communicated by Ronald Gould
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Authors |
| Darren B. Parker | |
| Department of Mathematics Grand Valley State University Allendale, MI United States |
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| Vasily Zadorozhnyy | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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