Abstract

The number of edges in a shortest walk from one vertex to another vertex of a connected graph G is known as the distance between them. For a vertex x and an edge e = a b in G, the minimum number from distances of x with a and b is said to be the distance between x and e. A vertex x is said to distinguish two distinct edges e 1 and e 2 if the distance between x and e 1 is different from the distance between x and e 2. A set X of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex in X. The number of vertices in such a smallest set X is known as the edge metric dimension of G. In this article, we solve the edge metric dimension problem for certain classes of planar graphs.