On atom bond sum connectivity index of chemical unicyclic graphs with a perfect matching

Abstract

The atom bond sum connectivity ($ABS$) index of a graph $\Gamma (V(\Gamma),E(\Gamma))$ is formulated by $ABS(\Gamma)=\sum_{xy\in E(\Gamma)}\sqrt{\frac{d_{\Gamma}(x)+d_{\Gamma}(y)-2}{d_{\Gamma}(x)+d_{\Gamma}(y)}}$, where $d_{\Gamma}(x)$ denotes the degree of vertex $x$ in $\Gamma$. In this work, we determine the maximum value of atom bond sum connectivity index of chemical unicyclic graphs with a perfect matching and identify the corresponding extremal graphs. Our discoveries extend the results of the recent paper [Wang et al., MATCH Commun. Math. Comput. Chem. 92 (2024) 653-669] from chemical trees with a perfect matching to chemical unicyclic graphs with a perfect matching.