| Naslov: | Maker-Breaker resolving game played on lexicographic products of graphs |
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| Avtorji: | ID Savitha, K. S. (Avtor)
ID Klavžar, Sandi (Avtor)
ID James, Tijo (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (288,44 KB)
MD5: 49A67CDE77698889A6AD674C465815E0
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s41980-026-01046-x
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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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| Ključne besede: | Maker-Breaker game, metric dimension, resolving set, Maker-Breaker resolving game, lexicographic product of graphs |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.04.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 12 str. |
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| Številčenje: | Vol. 52, iss. 2, article no. 21 |
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| PID: | 20.500.12556/DiRROS-28549  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 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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| Opomba: |
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| Datum objave v DiRROS: | 23.03.2026 |
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| Število ogledov: | 170 |
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| Število prenosov: | 109 |
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| Metapodatki: |    |
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