Extremal Trees for Sombor Index with Given Degree Sequence

Let G=(V, E) be a simple graph with vertex set V and edge set E. The Sombor index of the graph G is a degree-based topological index, defined as SO(G)= ∑uv∈E √(d(u)2+d(v)2), in which d(x) is the degree of the vertex x∈V for x=u, v. In this paper, we characterize the extremal trees with given degree sequence that minimizes and maximizes the Sombor index.