Majorization and the degree sequence of trees

TL;DR

This paper explores the relationship between degree sequences of trees and majorization order, establishing a necessary and sufficient condition for their comparability, and linking Lorenz curves with network degree sequences.

Contribution

It introduces a new theoretical framework connecting majorization, Lorenz curves, and tree degree sequences, with a key theorem on their comparability.

Findings

Proves a necessary and sufficient condition for degree sequence comparability in trees.

Links majorization theory with Lorenz curves and network degree sequences.

Enhances understanding of tree structures in data science.

Abstract

We investigate the relation between degree sequences of trees and the majorization order using the Muirhead theorem. In this way, we prove a theorem that provides a necessary and sufficient condition for delta sequences of trees to be comparable in the majorization order. Although our investigation is largely theoretical, our study contributes to a better knowledge of trees as an important data structure. We point out that this study is among the few combining Lorenz curves and majorization on the one hand, and degree sequences of networks on the other.