Extremal trees for Maximum Sombor index with given degree sequence

TL;DR

This paper characterizes the extremal trees with a fixed degree sequence that maximize the Sombor index, a degree-based topological measure, providing insights into graph structures with optimal properties.

Contribution

It introduces a characterization of extremal trees for the Sombor index given a degree sequence, a novel optimization problem in graph theory.

Findings

Identifies the structure of trees that maximize the Sombor index for a given degree sequence.

Provides a method to construct extremal trees with maximum Sombor index.

Enhances understanding of degree-based topological indices in graph optimization.

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.