Applied Mathematics and Computation vol:212 issue:2 pages:349-356
Let T be a weighted tree with n numbered leaves and let D (D(i,j))(i,j) be its distance matrix, so D(i,j) is the distance between the leaves i and j. If m is an integer satisfying 2 <= m <= n, we prove a tropical formula to compute the m-dissimilarity map of T (i.e. the weights of the subtrees of T with m leaves), given D. For m = 3, we present a tropical description of the set of m-dissimilarity maps of trees. For m = 4, a partial result is given. (C) 2009 Elsevier Inc. All rights reserved.