On Unicyclic Graph with Minimal Second Atom-Bond Connectivity Index

Abstract:

      Another version of atom-bond connectivity index was defined by Graovac and Ghorbani, and called the second atom-bond connectivity index($ABC_{2}$), which can provide convenience for molecular feature and its extreme values are the focus of study. In this paper, by fractional comparison, we give the structural properties of the extremal graphs which attain the minimal $ABC_{2}$ index of unicyclic graphs of order $n$.