From Vertex-Telecenters to Subtree-Telecenters

Zaw Win () and Cho Kyi Than ()
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Zaw Win: University of Yangon, Department of Mathematics
Cho Kyi Than: University of Yangon, Department of Mathematics

A chapter in Facets of Combinatorial Optimization, 2013, pp 163-174 from Springer

Abstract: Abstract Let T be a tree and v a vertex in T. It is well-known that the branch-weight of v is defined as the maximum number of vertices in the components of T−v and that a vertex of T with the minimum branch-weight is called a vertex-centroid of T. Mitchell (Discrete Math. 24:277–280, 1978) introduced a type of a central vertex called the telephone center or the vertex-telecenter of a tree and showed that v is a vertex-centroid of T if and only if it is a vertex-telecenter of T. In this paper we introduce the notions of the subtree-centroid and the subtree-telecenter of a tree which are natural extensions of the vertex-centroid and the vertex-telecenter, and generalize two theorems of Mitchell (Discrete Math. 24:277–280, 1978) in the extended framework of subtree-centroids and subtree-telecenters. As a consequence of these generalized results we also obtain an efficient solution method which computes a subtree-telecenter of a tree.

Keywords: Centroid Vertex; Branch Weight; Efficient Solution Procedure; Central Telephone; Discrete Math (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-38189-8_7

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