Abstract
The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively. For a vertex w and an edge f = c(1)c(2) of a connected graph G, the minimum number from distances of w with c(1) and c(2) is called the distance between w and f. If for every two distinct edges f(1), f(2) is an element of E(G), there always exists w(1) is an element of W-E subset of V(G) such that d(f(1), w(1)) not equal d(f(2), w(1)), then W-E is named as an edge metric generator. The minimum number of vertices in W-E is known as the edge metric dimension of G. In this paper, we calculate the edge metric dimension of ortho-polyphenyl chain graph O-n, meta-polyphenyl chain graph M-n, and the linear [n]-tetracene graph T[n] and also find the edge metric dimension of para-polyphenyl chain graph L-n. It has been proved that the edge metric dimension of O-n, M-n, and T[n] is bounded, while L-n is unbounded.