On the difference between atom-bond sum-connectivity index and Randić index of binary trees and chemical trees

Abstract

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 df 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.

Extremal Results and Bounds for Atom-Bond Sum-Connectivity Index

“…Upper bounds on the ABS index of n-order molecular trees in terms of the Randić index and n can be found in [62].…”