Majorization and the degree sequence of trees

Abstract

Objective. This study investigated the relation between the degree sequences of trees and the majorization order. Design/Methodology/Approach. The majorization technique was employed in accordance with the tenets of Muirhead’s theorem. Results. In this study, we proved a theorem that provides a necessary and sufficient condition for degree sequences of trees to be comparable in the majorization order. Research Limitations. Our research was focused on the study of trees rather than general networks. Furthermore, our investigation was primarily theoretical in nature. Practical Implications. Given the pervasiveness of trees in the field of information science, our theoretical study made a significant contribution to the advancement of knowledge regarding trees as a crucial data structure. Originality/Value. This study represented a rare instance of a text that combines two distinct but related areas of study: the Lorenz curves and majorization on the one hand and the degree sequences of networks on the other.