On weak metric dimension of digraphs

Abstract

Using the two-way distance, we introduce the concept of the weak metric dimension of a strongly connected digraph [Formula: see text]. We first establish lower and upper bounds for the number of arcs in [Formula: see text] by using the diameter and weak metric dimension of [Formula: see text], and characterize all digraphs attaining the lower or upper bound. Then we study a digraph with weak metric dimension 1 and classify all vertex-transitive digraphs having weak metric dimension 1. Finally, all digraphs of order n with weak metric dimension [Formula: see text] or [Formula: see text] are determined.