Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set {1,...,n}. For any i_1,..., i_k in {1,...,n}, define D_{i_1,....,i_k}(T) to be the sum of the lengths of the edges of the minimal subtree joining i_1,....,i_k. 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 families of real numbers that are the families of the multi-weights of a tree.
On dissimilarity vectors of general weighted trees / E. Rubei. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 312 (19):(2012), pp. 2872-2880. [10.1016/j.disc.2012.06.001]
On dissimilarity vectors of general weighted trees
RUBEI, ELENA
2012
Abstract
Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set {1,...,n}. For any i_1,..., i_k in {1,...,n}, define D_{i_1,....,i_k}(T) to be the sum of the lengths of the edges of the minimal subtree joining i_1,....,i_k. 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 families of real numbers that are the families of the multi-weights of a tree.File | Dimensione | Formato | |
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