  Two vertices u,v of connected graph G are doubly resolved by x,y\in V(G)if
d(v; x)-d(u; x)\neq d(v; y)-d(u; y): A set W of vertices of the graph G is a
doubly resolving set for G if every two distinct vertices of G are doubly
resolved by some two vertices of W. \psi(G) is the minimum cardinality of a
doubly resolving set for the graph G. The aim of this paper is to investigate
doubly resolving sets in graphs. An upper bound for \Psi(G) is obtained in
terms of order and diameter of G. \psi (G) is computed for some important
graphs and all graphs G of order n with the property \psi(G)=n-1 are
characterized.
