Mutual-Visibility Sets in Cartesian Products of Paths and Cycles

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.