Sets of Double and Triple Weights of Trees

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Sets of double and triple weights of trees

Abstract. Let T be a weighted tree with n leaves numbered by the set {1, ..., n}. Let Di,j be the distance between the leaves i and j. Let Di,j,k = 1 2 (Di,j +Dj,k +Di,k). We will call such numbers “triple weights” of the tree. In this paper, we find necessary and sufficient conditions for a set of real numbers indexed by 3-subsets of an n-set to be the set of the triple weights of a tree with ...

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ژورنال

عنوان ژورنال: Annals of Combinatorics

سال: 2011

ISSN: 0218-0006,0219-3094

DOI: 10.1007/s00026-011-0118-1