Metric Dimension of Line Graphs of Bakelite and Subdivided Bakelite Network

Abstract

Graph theory is considered one of the major subjects, and it also plays a significant role in the digital world. It has numerous uses in computer science, robot navigation, and chemistry. Graph theory is employed in forming the structures of different chemical networks, locating robots on a network, and troubleshooting computer networks. Additionally, it finds applications in scheduling airplanes and studying diffusion mechanisms. The current work investigates the metric dimension of the line graphs of the Bakelite and subdivided Bakelite networks. The results prove that these families of graphs do not have a constant metric dimension. The invention of Bakelite was influential in the development of modern plastics, and it has various applications in fields such as jewelry, clocks, toys, kitchenware, electrical, and sports industries.