On difference between atom-bond sum-connectivity index and Randić index of graphs

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)=∑fg∈ E(G) {1}{√d_fd_g(d_f+d_g)} (√d_fd_g(d_f+d_g-2)-√d_f+d_g), 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.