Mutual-Visibility Sets in Cartesian Products of Paths and Cycles
Danilo Korže, Aleksander Vesel · Results in Mathematics · 2024
Abstract For a given graph G , the mutual-visibility problem asks for the largest set of vertices $$M \subseteq V(G)$$ M ⊆ V ( G ) with the property that for any pair of vertices $$u,v \in M$$ 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.