On comb product graphs with respect to the complement metric dimension

Abstract

The complement metric dimension of graph is one of the recent topics in graph theory. The concept came from the metric dimension which is a topic that has developed very rapidly. The complement metric dimension of graph G is denoted by dmi(G). The goal of this research is to determine complement metric dimension of comb product of special graphs, such as path graph (Pn), star graph (S.,), and complete graph (Kn). Furthermore, we find complement metric dimension of comb product of any graphs G and H. We get that complement metric dimension of comb product of graph G and H depends on the order of both graph and complement metric dimension of graph H.