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Abstract: Let T be a weighted tree with n leaves. Let D {i,j} be the distance betweenthe leaves i and j. Let D {i,j,k}= D {i,j} + D {j,k} +D {i,k}-2. We will callsuch numbers -triple weights- of the tree. In this paper, we give acharacterization, different from the previous ones, for sets indexed by2-subsets of a $n$-set to be double weights of a tree. By using the sameideas,we find also necessary and sufficient conditions for a set of realnumbers indexed by 3-subsets of an $n$-set to be the set of the triple weightsof a tree with $n$ leaves. Besides we propose a slight modification ofSaitou-Nei-s Neighbour-Joining algorithm to reconstruct trees from the dataD {i,j}.



Author: Elena Rubei

Source: https://arxiv.org/



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