Maker-Breaker resolving game played on lexicographic products of graphs

Savitha, K. S. (avtor), Klavžar, Sandi (avtor), James, Tijo (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Maker-Breaker game, metric dimension, resolving set, Maker-Breaker resolving game, lexicographic product of graphs
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.04.2026
• Leto izida: 2026
• Št. strani: 12 str.
• Številčenje: Vol. 52, iss. 2, article no. 21
• PID: 20.500.12556/RUL-181037
• UDK: 519.17
• ISSN pri članku: 1018-6301
• DOI: 10.1007/s41980-026-01046-x
• COBISS.SI-ID: 272611587
• Datum objave v RUL: 23.03.2026

Gradivo je del revije

• Naslov: Bulletin of the Iranian Mathematical Society
• Skrajšan naslov: Bull. iran. math. soc.
• Založnik: Iranian Mathematical Society, Springer
• ISSN: 1018-6301
• COBISS.SI-ID: 518040345

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: igra izdelovalec-lomilec, metrična dimenzija, solventna množica, solventna igra izdelovalec-lomilec, leksikografski produkt grafov