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Title:
Bounds for the Atom-Bond Sum-Connectivity Index of Graphs
Authors:
Zaryab Hussain, Hechao Liu, Hongbo Hua
Volume
94
Issue
3
Year
2025
Pages
805-824
Abstract

The atom-bond sum-connectivity (\(ABSC\)) index of a graph \(G\) is defined as \(ABSC(G)=\sum\limits_{uv\in E(G)}\sqrt\frac{d_u+d_v-2}{d_u+d_v}\), where \(d_{u}\) and \(d_{v}\) represent the degrees of \(u\) and \(v\) in \(G\), respectively. In this paper, we give some sharp bounds for the \(ABSC\) index in terms of the first Zagreb index, the harmonic index, the sum-connectivity index, the minimum and maximum degrees, the clique number, and the chromatic number. We also find a lower bounds for the \(ABSC\) index of trees with given number of vertices and maximum degree.