Kannan Aarthi

Topological indices are numerical graph invariants generated from molecular graphs of chemicals to explain their structural properties. The atom-bond sum-connectivity (ABS) index and Randić (R) index are among the widespread graph invariants. The central theme of this work is the difference between these two indices, which is formulated for a graph G as ABS(G)-R(G)=\sum\limits_{fg\in E(G)} \dfrac{1}{\sqrt{d_fd_g(d_f+d_g)}} \left(\sqrt{d_fd_g(d_f+d_g-2)}-\sqrt{d_f+d_g}\right), where d_f stands for the degree of the vertex f in graph G. The primary objective of the article is to identify extremals over the set of all binary trees and chemical trees for ABS(G)-R(G). Furthermore, we aim to examine the significance of ABS(G)-R(G) in the structure-property modelling of molecules.