On the augmented Sombor index of graph operations

The augmented Sombor index ([Formula: see text]) is a recently introduced vertex-degree-based topological descriptor that has found promising applications in predicting the physicochemical properties of chemical compounds. For a connected graph [Formula: see text] with no edge joining two vertices of degree [Formula: see text], it is defined by [Formula: see text] where [Formula: see text] denotes the degree of vertex [Formula: see text]. In this paper, we explore the behavior of this index under fundamental graph operations such as the join, corona, Cartesian product, and lexicographic product. We also establish sharp upper and lower bounds for the augmented Sombor index of these graph operations in terms of fundamental graph parameters.