| Title: | Maker-Breaker resolving game played on corona products of graphs |
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| Authors: | ID James, Tijo (Author)
ID Klavžar, Sandi (Author)
ID Kuziak, Dorota (Author)
ID Savitha, K. S. (Author)
ID Vijayakumar, Ambat (Author) |
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| Files: |  PDF - Presentation file, download (284,05 KB)
MD5: BE5431CE523BEE4C644A84B84A47D1AF
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00010-024-01132-7
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 $2$. |
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| Keywords: | Maker-Breaker game, resolving set, Maker-Breaker resolving game, Maker-Breaker resolving number, corona product of graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.06.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1221-1233 |
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| Numbering: | Vol. 99, iss. 3 |
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| PID: | 20.500.12556/DiRROS-23899  |
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| UDC: | 519.17 |
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| ISSN on article: | 0001-9054 |
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| DOI: | 10.1007/s00010-024-01132-7 |
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| COBISS.SI-ID: | 238692355 |
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| Note: |
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| Publication date in DiRROS: | 20.10.2025 |
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| Views: | 179 |
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| Downloads: | 107 |
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