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Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility setif each pair of vertices from $X$ is connected by a geodesic with no internalvertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinalityof a largest mutual-visibility set. In this paper, the mutual-visibility numberof strong product graphs is investigated. As a tool for this, totalmutual-visibility sets are introduced. Along the way, basic properties of suchsets are presented. The (total) mutual-visibility number of strong products isbounded from below in two ways, and determined exactly for strong grids ofarbitrary dimension. Strong prisms are studied separately and a couple of tightbounds for their mutual-visibility number are given.

Mutual-visibility in strong products of graphs via total mutual-visibility