On Metric Dimension of Circumcoronene Series of Benzenoid Networks

Abstract

In molecular topology and chemistry, resolving sets and metric bases are essential concepts. They have numerous applications in computer science, artificial intelligence, chemistry, pharmacy, traffic networking, mathematical modeling, and programming. Adivision S of the vertex set chi of a linked graph G is said to resolve G if eachpoint of G can be represented from its neighborhood in S. A metric dimension of a graph is the number of the smallest resolving set, also known as the metric basis of the graph.In the current research we will determine the metric dimension and metric basis of the circumcoronene series CS of benzenoid Hk for k >= 1. We prove that a set with three vertices is required to resolve this graph, and therefore, its metric dimension is 3.