Extremal values of the atom-bond sum-connectivity index in bicyclic graphs

Let G be a graph with V(G) and E(G), as vertex set and edge set respectively. The atom-bond sum-connectivity index is a degree-based topological index which is defined as ABS(G)=∑uv∈E(G)du+dv-2du+dv,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} ABS(G)=\sum \limits _{uv\in E(G)}\sqrt{\dfrac{d_u+d_v-2}{d_u+d_v}}, \end{aligned}$$\end{document}where the degree of the vertex u is denoted by du\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_u$$\end{document}. In this article, our focus lies on investigating the maximum value of atom-bond sum-connectivity among the class of bicyclic graphs on n vertices. In addition, the role of atom-bond sum-connectivity in explaining structure–property relationship is also demonstrated.