2023/07/05 by Cong X. Kang, Kang, Cong X., Kelenc, Aleksander +1 · 1 citation
Computer Science · Mathematics · Social Sciences · #05C12 #05C57 #05C70 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Japanese History and Culture #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2307.02373
openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a graph with vertex set V. A set S ⊆ V is a strong resolving set of G if, for distinct x,y∈ V, there exists z∈ S such that either x lies on a y-z geodesic or y lies on an x-z geodesic in G. In this paper, we study maker-breaker strong resolving game (MBSRG) played on a graph by two players, Maker and Breaker, where the two players alternately select a vertex of G not yet chosen. Maker wins if he is able to choose vertices that form a strong resolving set of G and Breaker wins if she is able to prevent Maker from winning in the course of MBSRG. We denote by O\rm SR(G) the outcome of MBSRG played on G. We obtain some general results on MBSRG and examine the relation between O\rm SR(G) and O\rm R(G), where O\rm R(G) denotes the outcome of the maker-breaker resolving game of G. We determine the outcome of MBSRG played on some graph classes, including corona product graphs, Cartesian product graphs, and modular product graphs.