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 details Title Optimizing quadratic forms of adjacency matrices of trees AbstractLet G=(V,E) be a tree with n vertices. For n nonnegative numbers x1>= x2 ... >= xn>= 0, there exists a mapping \sigma: V --> {x1,...,xn} which maximizes $\sum \sigma(v)\sigma(w)$, where the sum is over all the edges (v,w) of G . A necessary and sufficient condition is determined for \sigma to be independent of the choice of xi's, and it leads to a corresponding solution for the following problem: Maximize the largest eigenvalue of PDPt+A over a permutation matrix P, where D is a nonnegative diagonal matrix and A is the adjacency matrix of a tree. Speaker(s) Wai-Shun Cheung (Centro de Estruturas Lineares e Combinatórias, Universidade de Lisboa, Portugal) Date May 22, 2002Time15:00 Room Sala 5.5 CMUC Apartado 3008, 3001 - 454 Coimbra, Portugal T:+351 239 791 150 F:+351 239 793 069 cmuc@mat.uc.pt - developed by Flor de Utopia