Maker-Breaker resolving game played on corona products of graphs

The Maker-Breaker resolving game is a game played on a graph G by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex of G. The goal of Resolver is to select all the vertices in a resolving set of G, while that of Spoiler is to prevent this from happening. The outcome o(G) of the game played is one of \(\mathcal {R}\), \(\mathcal {S}\), and \(\mathcal {N}\), where \(o(G)=\mathcal {R}\) (resp. \(o(G)=\mathcal {S}\)), if Resolver (resp. Spoiler) has a winning strategy no matter who starts the game, and \(o(G)=\mathcal {N}\), if the first player has a winning strategy. In this paper, the game is investigated on corona products \(G\odot H\) of graphs G and H. It is proved that if \(o(H)\in \{\mathcal {N}, \mathcal {S}\}\), then \(o(G\odot H) = \mathcal {S}\). No such result is possible under the assumption \(o(H) = \mathcal {R}\). It is proved that \(o(G\odot P_k) = \mathcal {S}\) if \(k=5\), otherwise \(o(G\odot P_k) = \mathcal {R}\), and that \(o(G\odot C_k) = \mathcal {S}\) if \(k=3\), otherwise \(o(G\odot C_k) = \mathcal {R}\). Several results are also given on corona products in which the second factor is of diameter at most 2.