On Metric Dimension of Edge Comb Product of Symmetric Graphs

Abstract

Consider a finite graph G that is simple, undirected, and connected. Let W be an ordered set of vertices with |W| = k. The representation of a vertex v is defined as an ordered k-tuple that consists of the distances from vertex v to each vertex in W. The set W is called a resolving set for G if the k-tuples for any two vertices in G are distinct. The metric dimension of G, denoted by dim(G), is the smallest possible size of such a set W. In this paper, we determine the metric dimension of edge comb product of trees with complete multipartites or petersen graphs.

Keywords

• edge comb product
• symmetric
• metric dimension