A characterization of dissimilarity families of trees

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• 作者：Agnese Baldisserri ; Elena Rubei ; ^{rubei@math.unifi.it}
• 关键词：Weighted trees ; Dissimilarity families
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：31 March 2017
• 年：2017
• 卷：220
• 期：Complete
• 页码：35-45
• 全文大小：460 K
• 卷排序：220

文摘

Let T=(T,w)T=(T,w) be a weighted finite tree with leaves 1,…,n1,…,n. For any I≔{i1,…,ik}⊂{1,…,n}I≔{i1,…,ik}⊂{1,…,n}, let DI(T)DI(T) be the weight of the minimal subtree of TT connecting i1,…,iki1,…,ik; the DI(T)DI(T) are called kk-weights of TT. Let {DI}Ik-subset of {1,…,n} be a family of real numbers. We say that a weighted tree T=(T,w)T=(T,w) with leaves 1,…,n1,…,n realizes the family if DI(T)=DIDI(T)=DI for any kk-subset II of {1,…,n}{1,…,n}.In this paper we find some equalities and inequalities characterizing the families of real numbers parametrized by the kk-subsets of {1,…,n}{1,…,n} that are the families of kk-weights of weighted trees whose leaf set is equal to {1,…,n}{1,…,n} and whose weights of the internal edges are positive (where we say that an edge ee is internal if there exists a path with endpoints of degree greater than 2 and containing ee).