First irregularity Sombor index of trees with fixed maximum degree

The Sombor index as a new degree-based topological index was first put forward in 2021 by Gutman. Recently, Kulli introduced a variant of the Sombor index called first irregularity Sombor index. The first irregularity Sombor index of a graph G, denoted by (Formula presented.), is defined as the sum of weights (Formula presented.) of all edges vw of E(G), where (Formula presented.) denotes the degree of a node v in G. In this paper we show that for any tree T of order n with maximum degree Δ, (Formula presented.) We also characterize the extremal trees.