Sets of double and triple weights of trees [article]

Elena Rubei
2011 arXiv   pre-print
Let T be a weighted tree with n leaves. Let D_i,j be the distance between the leaves i and j. Let D_i,j,k= (D_i,j + D_j,k +D_i,k)/2. We will call such numbers "triple weights" of the tree. In this paper, we give a characterization, different from the previous ones, for sets indexed by 2-subsets of a n-set to be double weights of a tree. By using the same ideas,we find also 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
more » ... eights of a tree with n leaves. Besides we propose a slight modification of Saitou-Nei's Neighbour-Joining algorithm to reconstruct trees from the data D_i,j.
arXiv:0712.3026v3 fatcat:qsxbzinqfrbjnnvzz7dcl3qa3u