In this article, we determine the extremal graphs concerning the augmented Sombor index over the connected graph (resp. chemical graph) of a given order. Then we have determined several upper and lower bounds on the augmented Sombor index of a graph with given parameters. Finally, in Sec. 3, we determine the relationships between the augmented Sombor index and other standard topological indices and also characterize the family of graphs where the bounds are reached.
Khanra et al. (Wed,) studied this question.