Let d be a positive integer. The mutual d-visibility number \({\mu ^d}(G)\) of a graph G is introduced as the cardinality of the largest mutual d-visibility set. That is, \(X\subseteq V(G)\) is a mutual d-visibility set if for any pair of vertices \(x,y\in X\) , the distance between them is larger than d, or there exists a shortest x, y-path in G whose internal vertices are not in X. Several combinatorial and computational aspects of \({\mu ^d}(G)\) are given in this work. Finally, the NP-completeness of the decision problem concerning finding \({\mu ^d}(G)\) is proved.
