On The Geodesic Identification Of Vertices In Convex Plane Graphs

A shortest path between two vertices u and v in a connected graph G is a u - v geodesic. A vertex w of G performs the geodesic identification for the vertices in a pair (u, v) if either v belongs to a u - w geodesic or u belongs to a v - w geodesic. The minimum number of vertices performing the geodesic identification for each pair of vertices in G is called the strong metric dimension of G. In this paper, we solve the strong metric dimension problem for three convex plane graphs by performing the geodesic identification of their vertices.