Geometric Arithmetic Index of Alkanes and Unicyclic chemical graphs

Abstract

The Geometric–Arithmetic (GA) index has emerged as one of the most actively studied degree-based molecular structure descriptors due to its significant relevance in chemical graph theory. For a graph Γ, the GA index is given by GA(Γ) =P_μν∈E(Γ) (2√λμλν)/(λμ+λν). Here, λμ denotes the degree of the vertex μ in the graph Γ. In this research, we develop general expressions for the Geometric–Arithmetic index for various families of trees and uni–cyclic graphs, with illustrative applications to chemical structures such as alkanes, their isomers, and broader classes of cycloalkanes.