Sombor Index of Non-coprime Graphs on Generalized Quaternion Groups

Abstract

This research presents the general formulation of the Sombor index as topological descriptors in the context of non-coprime graphs constructed from generalized quaternion group. The main objective is to determine closed-form expressions for these indices by analyzing the structural properties of the graph constructed from group elements whose orders are not coprime. Through this investigation, general formulas for the Sombor index and its derivatives are successfully derived, highlighting the interplay between algebraic structures and graph-theoretic measures in non-abelian settings