Maker-Breaker resolving game played on corona products of graphs

James, Tijo (author), Klavžar, Sandi (author), Kuziak, Dorota (author), Savitha, K. S. (author), Vijayakumar, Ambat (author)

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 $2$.

• Language: English
• Keywords: Maker-Breaker game, resolving set, Maker-Breaker resolving game, Maker-Breaker resolving number, corona product of graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 1221-1233
• Numbering: Vol. 99, iss. 3
• PID: 20.500.12556/RUL-169827
• UDC: 519.17
• ISSN on article: 0001-9054
• DOI: 10.1007/s00010-024-01132-7
• COBISS.SI-ID: 238692355
• Publication date in RUL: 12.06.2025

Record is a part of a journal

• Title: Aequationes mathematicae
• Shortened title: Aequ. math.
• Publisher: Springer
• ISSN: 0001-9054
• COBISS.SI-ID: 1327364

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: igra izdelovalec-lomilec, solventna množica, solventna igra izdelovalec-lomilec, solventno število izdelovalec-lomilec, koronski produkt grafov