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Centroids to centers in trees
Author(s) -
Reid K. B.
Publication year - 1991
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.3230210103
Subject(s) - combinatorics , vertex (graph theory) , mathematics , centroid , ball (mathematics) , integer (computer science) , radius , graph , geometry , computer science , computer security , programming language
If k is a nonnegative integer and x is a vertex of a tree T , the k ‐ball branch weight of x , denoted b(x;k) , is the number of vertices in a largest subtree of T , all of whose vertices are a distance at least k + 1 from x . The k ‐ball branch weight centroid of T , denoted W(T;k) , consists of all vertices x of T for which b(x;k) is a minimum. The usual branch weight centroid of T (which is also the median) is W ( T ;0), and the center of T is W(T;r) , where r is the radius of T . In this paper, the structure of the subgraph spanned by W(T;k) is examined. Similarities and differences with Slater's k ‐centrum [6] and k ‐nucleus [7] are discussed.