The Augmented Sombor index of a connected graph \( G \) with at least three vertices is defined as \[ ASO(G) = \sum_{v_i v_j \in E(G)} \sqrt{\frac{d_i^2 + d_j^2}{d_i + d_j - 2}}, \] where \( d_i \) and \( d_j \) denote the degrees of the vertices \( v_i \) and \( v_j \), respectively.
In this paper, we examine the chemical applicability of the \( ASO \) index for predicting thirteen physicochemical properties of octane isomers. We also characterize extremal graphs with respect to the \( ASO \) index over the following three classes of graphs with a given order: (i) trees, (ii) quasi-trees (where a quasi-tree is a connected graph that becomes a tree upon the removal of a single vertex), and (iii) connected graphs. Furthermore, we determine the unique graph minimizing the \( ASO \) index among all unicyclic graphs of fixed order. Finally, we conclude the paper by outlining potential directions for future research related to the \( ASO \) index.