Lit-only sigma-game on nondegenerate graphs
Hau-wen Huang

TL;DR
This paper characterizes the behavior of the lit-only sigma-game on nondegenerate, non-line graphs, showing they are 2-lit and providing criteria for 1-lit status using linear algebra.
Contribution
It offers a complete description of the game dynamics on certain graphs and introduces a linear algebraic condition for 1-lit graphs, expanding understanding of the game.
Findings
Nondegenerate, non-line graphs are 2-lit.
Provided a linear algebraic criterion for 1-lit graphs.
Described the orbits of the game on these graphs.
Abstract
A configuration of the lit-only -game on a graph is an assignment of one of two states, {\it on} or {\it off}, to each vertex of Given a configuration, a move of the lit-only -game on allows the player to choose an {\it on} vertex of and change the states of all neighbors of Given an integer , the underlying graph is said to be -lit if for any configuration, the number of {\it on} vertices can be reduced to at most by a finite sequence of moves. We give a description of the orbits of the lit-only -game on nondegenerate graphs which are not line graphs. We show that these graphs are 2-lit and provide a linear algebraic criterion for to be 1-lit.
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Taxonomy
TopicsArtificial Intelligence in Games · Cellular Automata and Applications · Computability, Logic, AI Algorithms
