Mutual-Visibility Sets in Cartesian Products of Paths and Cycles

Abstract For a given graph G, the mutual-visibility problem asks for the largest set of vertices M V (G) M ⊆ V (G) with the property that for any pair of vertices u, v M u, v ∈ M there exists a shortest u, v -path of G that does not pass through any other vertex in M. The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.