Vol. 14, No. 4, 2021

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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
Abstract

The Lights Out game, originally an electronic game played on a 5×5 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 n. We define a new variant of the Lights Out game, where the vertex labels can come from any group H. This new game depends deeply on the group structure of H and gives us a significantly different game for cyclic groups. We investigate problems related to counting winnable labelings in the case H = n.

Keywords
Lights Out, vertex labeling, games on graphs
Mathematical Subject Classification 2010
Primary: 05C20, 06B99
Milestones
Received: 6 November 2017
Revised: 19 June 2018
Accepted: 19 June 2020
Published: 23 October 2021

Communicated by Ronald Gould
Authors
Darren B. Parker
Department of Mathematics
Grand Valley State University
Allendale, MI
United States
Vasily Zadorozhnyy
Department of Mathematics
University of Kentucky
Lexington, KY
United States