Classes of Planar Graphs with Constant Edge Metric Dimension

The number of edges in a shortest walk (without repetition of vertices) 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=ab 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 (resolves) 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.

Automated summary

The edge metric dimension of a graph refers to the number of vertices in the smallest set X that can distinguish every two edges in the graph. In this article, the authors solve the edge metric dimension problem for certain classes of planar graphs.