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Majorization and distances in trees
Author(s) -
Dahl Geir
Publication year - 2007
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20202
Subject(s) - majorization , combinatorics , vertex (graph theory) , center (category theory) , mathematics , tree (set theory) , discrete mathematics , graph , chemistry , crystallography
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