On the Generalized ABS Index of Graphs

Abstract

The atom-bond sum-connectivity ($ABS$) index is a recently introduced variant of three earlier much-studied graph-based molecular descriptors: Randi\'c, atom-bond connectivity, and sum-connectivity indices.
The general atom-bond sum-connectivity index is defined as $ABS_\alpha(G) =\sum_{uv\in E(G)}\left( \frac{d_u+d_v-2}{d_u+d_v} \right) ^{\alpha}$, where $\alpha$ is a real number.
In this paper, we present some upper and lower bounds on the general atom-bond sum-connectivity index in terms of graph parameters and other graph indices.