On the Geodesic Identification of Vertices in Convex Plane Graphs

Abstract EN

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.