The w-centroids and least w-central subtrees in weighted trees

Erfang Shan () and Liying Kang ()
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Erfang Shan: Shanghai University
Liying Kang: Shanghai University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 4, No 2, 1118-1127

Abstract: Abstract Let T be a weighted tree with a positive number w(v) associated with each vertex v. A subtree S is a w-central subtree of the weighted tree T if it has the minimum eccentricity $$e_L(S)$$ e L ( S ) in median graph $$G_{LW}$$ G L W . A w-central subtree with the minimum vertex weight is called a least w-central subtree of the weighted tree T. In this paper we show that each least w-central subtree of a weighted tree either contains a vertex of the w-centroid or is adjacent to a vertex of the w-centroid. Also, we show that any two least w-central subtrees of a weighted tree either have a nonempty intersection or are adjacent.

Keywords: Tree; w-centroid; w-central subtree; Least w-central subtree; 05C05; 05C22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0174-5

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