Let \(G=(V(G),E(G))\) be a connected graph and \(d(f,y)\) denotes the distance between edge \(f\) and vertex \(y\), which is defined as \(d(f,y) = \min \{d(p,y),d(q,y)\}\), where \(f=pq\). A subset \(W_E \subseteq V(G)\) is called an edge metric generator for graph \(G\) if for every two distinct edges \(f_1, f_2 \in E(G)\), there exists a vertex \(y\in W_E\) such that \(d(f_1,y) \neq d(f_2,y)\). An edge metric generator with minimum number of vertices is called an edge metric basis for graph \(G\) and the cardinality of an edge metric basis is called the edge metric dimension represented by \(edim(G)\). In this paper, we study the edge metric dimension of flower graph \({f}_{n\times 3}\) and also calculate the edge metric dimension of the prism related graphs \(D_{n}^{'}\) and \(D_{n}^{t}\). It has been concluded that the edge metric dimension of \(D_{n}^{'}\) is bounded, while of \({f}_{n\times 3}\) and \(D_{n}^{t}\) is unbounded.

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 and an edge of a connected graph , the minimum number from distances of with and is called the distance between and . If for every two distinct edges , there always exists such that , then is named as an edge metric generator. The minimum number of vertices in is known as the edge metric dimension of . In this paper, we calculate the edge metric dimension of ortho-polyphenyl chain graph , meta-polyphenyl chain graph , and the linear [n]-tetracene graph and also find the edge metric dimension of para-polyphenyl chain graph . It has been proved that the edge metric dimension of , , and is bounded, while