The doubly resolving number of the lexicographic product of graphs

Two vertices [Formula: see text] in a connected graph [Formula: see text] are doubly resolved by vertices [Formula: see text] of [Formula: see text] if [Formula: see text] A set [Formula: see text] of vertices of the graph [Formula: see text] is a doubly resolving set for [Formula: see text] if every two distinct vertices of [Formula: see text] are doubly resolved by some two vertices of [Formula: see text]. Doubly resolving number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of a doubly resolving set for [Formula: see text]. The aim of this paper is to investigate doubly resolving sets in the lexicographic product graphs. It is proved that if [Formula: see text] or [Formula: see text] does not have any vertex of degree [Formula: see text], then [Formula: see text]. Also [Formula: see text] is computed in other cases.