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.