20.500.12556/RUL-181037 Maker-Breaker resolving game played on lexicographic products of graphs 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. Maker-Breaker game metric dimension resolving set Maker-Breaker resolving game lexicographic product of graphs igra izdelovalec-lomilec metrična dimenzija solventna množica solventna igra izdelovalec-lomilec leksikografski produkt grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-23 14:26:08 2026-03-23 14:26:13 2026-03-24 04:26:38 0000-00-00 00:00:00 2026 0 0 12 str. iss. 2, article no. 21 Vol. 52 Apr. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-04-01 519.17 1018-6301 10.1007/s41980-026-01046-x 272611587 s41980-026-01046-x.pdf s41980-026-01046-x.pdf 1 1B46DB017F824400D480F3547CE916D8 32d1b921a84d08534ea796a0ce4851436b215b2c4120cd21fff25f31d45c075c 5db68b73-26bc-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231131 https://link.springer.com/article/10.1007/s41980-026-01046-x 1 c35a4074-26bb-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231129 Fakulteta za matematiko in fiziko 0 0 0