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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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