Degree and Distance-based topological indices of power graphs of finite non-abelian groups

Abstract

Topological indices can be used to characterize molecular topology. These are numerical measurements of a suggested molecule’s fundamental structural characteristics, derived from its molecular structure. This numerical value, which is derived from a chemical configuration, represents the important physical properties of the proposed molecule. We use an algebraic number to connect the chemical composition with various physical characteristics, biological activity, and chemical reactivity. A graph with a vertex set of [Formula: see text] in which two unique vertices are adjacent when one element is an integral power of the other is called a power graph [Formula: see text] of a finite group [Formula: see text]. This paper investigates several types of topological indices of power graphs for different finite groups based on distance, degree, and independent sets. We compute the Hyper Wiener Index, Degree Distance Index, Additively Weighted Harary Index, Gutman Index, Multiplicatively Weighted Harary Index, Eccentric Connectivity Index, Connective Eccentricity Index, and Merrifield Simmons Index of power graphs for finite cyclic and non-cyclic groups of order [Formula: see text], dihedral and generalized quaternion groups, where [Formula: see text] are distinct primes. As a consequence, we fix the flaws in the results of [5] and present their correct forms.