On the Sombor index of trees with degree restrictions

TL;DR

This paper investigates the Sombor index in trees with degree restrictions, identifying extremal trees and characterizing all trees with maximum or minimum index values, along with comparative analyses and corollaries.

Contribution

It provides a complete characterization of trees with extremal Sombor index values under degree constraints, extending previous results and offering new insights.

Findings

Greedy trees minimize the Sombor index among trees with a given degree sequence.

Alternating greedy trees maximize the Sombor index among such trees.

The paper offers a full characterization of all extremal trees and compares different degree sequences.

Abstract

We study the Sombor index of trees with various degree restrictions. In addition to rediscovering that among all trees with a given degree sequence, the greedy tree minimises the Sombor index and the alternating greedy tree maximises it, we also provide a full characterisation of all trees that have those maximum or minimum values. Moreover, we compare trees with different degree sequences and deduce a few corollaries.