20.500.12556/RUL-163141 Mutual-visibility in strong products of graphs via total mutual-visibility Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given. mutual-visibility set mutual-visibility number total mutual-visibility set strong product of graphs množica vzajemne vidnosti število vzajemne vidnosti množica celotne vzajemne vidnosti krepki produkt grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2024-10-02 15:00:37 2024-10-02 15:00:40 2024-10-07 03:39:34 0000-00-00 00:00:00 2024 0 0 Str. 136-146 Vol. 358 Dec. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-12-01 519.17 0166-218X 10.1016/j.dam.2024.06.038 201822467 1-s2.0-S0166218X24002907-main.pdf 1-s2.0-S0166218X24002907-main.pdf 1 1FF2D4123EC505ED6452BFCE80E0F483 c02943d027faf9d91d5d6f4c948e3ab1d9f96a5c93e96452bb0e41d2aeeaa800 f2c3a64a-80be-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=192647 https://www.sciencedirect.com/science/article/pii/S0166218X24002907 1 2c03139b-80be-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=192646 Fakulteta za matematiko in fiziko 0 0 0