Minimizing the Sombor Index among Trees with Fixed Degree Sequence

TL;DR

This paper investigates the Sombor index, a vertex-degree-based topological measure, and identifies the tree structure that minimizes this index for a fixed degree sequence, advancing understanding in mathematical chemistry.

Contribution

It proves that the greedy tree minimizes the Sombor index among all trees with a given degree sequence, addressing an open problem.

Findings

Greedy tree minimizes the Sombor index for fixed degree sequences.

Provides partial solution to the extremal problem for the Sombor index.

Enhances understanding of topological indices in chemical graph theory.

Abstract

Vertex-degree-based topological indices have recently gained a lot of attention from mathematical chemists. One such index that we focus on in this paper is called Sombor index. After its definition in late 2020, the Sombor index was quickly recognized as a valuable research topic. In this paper we partially answer the open question of finding the extremal trees with respect to this index for a fixed degree sequence. Particularly we focus on the lower bound and proceed to show that greedy tree minimizes the Sombor index for a given degree sequence.