Vertices, edges, distances and metric dimension in graphs

Abstract Given a connected graph G = ( V , E ) , a set of vertices S ⊂ V is an edge metric generator for G , if any two edges of G are identified by S by mean of distances to the vertices in S . Moreover, in a natural way, S is a mixed metric generator, if any two elements of G (vertices or edges) are identified by S by mean of distances. In this work we study the (edge and mixed) metric dimension of graphs.