On the minimum Sombor index of trees with a given independence number

The Sombor index of a graph [Formula: see text], introduced by Gutman in 2021, is a topological index based on vertex degrees. It is defined by [Formula: see text] where [Formula: see text] and [Formula: see text] denote the degrees of the end-vertices of edge [Formula: see text]. In this paper we provide a lower bound for the Sombor index of trees with a given independence number [Formula: see text] and order [Formula: see text], and characterize trees that achieve this bound. This study contributes to ongoing research on the extremal properties of the Sombor index and its relation to other graph parameters.