Abstract
In the modern digital sphere, graph theory is a significant field of research that has a great deal of significance. It finds widespread application in computer science, robotic directions, and chemistry. Additionally, graph theory is used in robot network localization, computer network problems and the formation of various chemical structures for networks. Moreover, it finds uses in exploring diffusion mechanisms and scheduling aircraft as well. The present research project examines and concentrates on the edge version of metric dimension of the Concealed Non-Kekuléan Benzenoid Hydrocarbon, Polythiophene, Backbone DNA network and Bakelite networks. All the mentioned networks have constant edge metric dimension except Bakelite network, as demonstrated by the results. If we talk about the applications of these networks, Polythiophene are used to treat prion disorders. It is also capable of detecting metal ions. The concept of Bakelite, which finds applications in the jewelry, electrical, cookware, sports, and clock industries, had an impact on the invention of modern polymers. The functions of DNA include information encoding, replication, mutation, and recombination gene expression.