Extremal trees for Maximum Sombor index with given degree sequence

Abstract

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 $$SO(G)=\sum _{uv\in E}\sqrt{d(u{)}^2+d(v{)}^2},$$ in which $d(x)$ is the degree of the vertex $x\in V$ for $x=u,v$. In this paper, we characterize the extremal trees with a given degree sequence that maximizes the Sombor index.