Rubei, Prof. Elena (2012) On dissimilarity vectors of (not necessarily positive) weighted trees. Technical Report 2012.01.02, no. 2, Dipartimento di Matematica "U.Dini", Universita' di Firenze.

Abstract

Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set {1, ..., n}. For any i1,...,ik ∈ {1,...,n}, define Di1,....,ik(T) as the sum of the lengths of the edges of the minimal subtree connecting i1,....,ik. We will call such numbers “k-weights” of the tree and we call the k-weights for any k ≥ 2 “multi-weights” of the tree. In this paper, we give a characterization of the sets of real numbers that are the sets of the multi-weights of a tree.