On the metric dimension of a class of planar graphs

Abstract

Let H = (V, E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices Rm from V (H) is said to be a resolving set for H if each vertex of H is uniquely determined by its vector of distances to the vertices of Rm. The number of vertices in a smallest resolving set is called the metric dimension of H. In this article, we study the metric dimension for a rotationally symmetric family of planar graphs, each of which is shown to have an independent minimum resolving set of cardinality three.