Majorization and distances in trees

✍ Scribed by Geir Dahl

• Book ID: 102547029
• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 158 KB
• Volume: 50
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/net.20202

✦ Synopsis

Abstract

We investigate distance vectors in trees and introduce a new center concept based on the notion of majorization and discuss relations to location theory. For a tree T and a vertex v ∈ T, we define the distance vector d(v,·) = (d(v,w) w ∈ T), where d(v,w) denotes the distance between v and a vertex w. We characterize whenever d(u,·) is weakly majorized by d(v,·) for adjacent vertices u and v. Moreover, we introduce a new center concept in trees, the majorization‐center, and relate this to known centers and the set of balance vertices. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(4), 251–257 2007