Maker-Breaker resolving game played on corona products of graphs
Tijo James, Sandi Klav\v{z}ar, Dorota Kuziak, Savitha K S, Ambat Vijayakumar

TL;DR
This paper studies the Maker-Breaker resolving game on corona product graphs, determining the game's outcome based on properties of the component graphs and providing specific results for paths and cycles.
Contribution
It characterizes the game outcome on corona products of graphs, especially for paths and cycles, and extends understanding of the game on graphs with diameter at most two.
Findings
If o(H) in {N, S}, then o(G⊙H) = S.
o(G⊙P_k) = S if k=5; otherwise R.
o(G⊙C_k) = S if k=3; otherwise R.
Abstract
The Maker-Breaker resolving game is a game played on a graph by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex of . The goal of Resolver is to select all the vertices in a resolving set of , while that of Spoiler is to prevent this from happening. The outcome of the game played is one of , , and , where (resp.\ ), if Resolver (resp.\ Spoiler) has a winning strategy no matter who starts the game, and , if the first player has a winning strategy. In this paper, the game is investigated on corona products of graphs and . It is proved that if , then . No such result is possible under the assumption . It is proved that…
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Taxonomy
TopicsArtificial Intelligence in Games · Educational Games and Gamification
