SOME CHEMICAL TOPOLOGICAL INDICES FOR THE COPRIME GRAPH OF THE INTEGERS MODULO GROUP

This paper delves into the exploration of the coprime graph of a finite group G, a graph with vertices representing all group elements. Vertices x and y are considered adjacent in ΓG if their orders are relatively prime. Specifically, our focus lies in determining essential topological indices: the first Zagreb index, the second Zagreb index, and the Wiener index of the coprime graph associated with the group of integers modulo n. The groups under consideration in this study are those of integers modulo n, where n takes the form of prime power and multiplication of two prime powers, with p and q representing distinct prime numbers and r and s representing natural numbers. This investigation aims to provide a comprehensive understanding of the structural and numerical properties of the coprime graph within the context of finite groups, shedding light on the intricate relationships between group elements and their algebraic properties.