Mutual-visibility in strong products of graphs via total mutual-visibilityCicerone, Serafino (Avtor) Di Stefano, Gabriele (Avtor) Klavžar, Sandi (Avtor) Yero, Ismael G. (Avtor) mutual-visibility setmutual-visibility numbertotal mutual-visibility setstrong product of graphsLet $G$ 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.20242024-10-02 15:00:37Članek v reviji163141UDK: 519.17ISSN pri članku: 0166-218XDOI: 10.1016/j.dam.2024.06.038COBISS_ID: 201822467sl