| Title: | Maker-Breaker resolving game played on lexicographic products of graphs |
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| Authors: | ID Savitha, K. S. (Author)
ID Klavžar, Sandi (Author)
ID James, Tijo (Author) |
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| Files: |  PDF - Presentation file, download (288,44 KB)
MD5: 49A67CDE77698889A6AD674C465815E0
 URL - Source URL, visit https://link.springer.com/article/10.1007/s41980-026-01046-x
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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: | In the Maker-Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph $G$. The aim of Resolver is to select all the vertices of some resolving set of $G$, while Spoiler aims to select at least one vertex from every resolving set of $G$. In this paper, this game is investigated on the lexicographic product of graphs. It is proved that if Spoiler has a winning strategy on a graph $H$ no matter who starts the game, or if the first player has a winning strategy on $H$, then Spoiler always has a winning strategy on $G\circ H$. Special attention is paid to lexicographic products in which the second factor is a complete graph, a path, or a cycle. For instance, in $G\circ P_{2\ell}$ and in $G\circ C_{2\ell}$, Resolver always wins, while in $G\circ P_{2\ell+1}$ and in $G\circ C_{2\ell+1}$ the same conclusion holds provided $G$ is free from false twins. On the other hand, Spoiler always wins on $G\circ P_5$. In most of the cases, the corresponding Maker-Breaker resolving number is also determined. |
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| Keywords: | Maker-Breaker game, metric dimension, resolving set, Maker-Breaker resolving game, lexicographic 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: | 01.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 12 str. |
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| Numbering: | Vol. 52, iss. 2, article no. 21 |
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| PID: | 20.500.12556/DiRROS-28549  |
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| UDC: | 519.17 |
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| ISSN on article: | 1018-6301 |
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| DOI: | 10.1007/s41980-026-01046-x |
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| COBISS.SI-ID: | 272611587 |
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| Note: |
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| Publication date in DiRROS: | 23.03.2026 |
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| Views: | 167 |
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| Downloads: | 107 |
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| Metadata: |    |
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