Algebra and Combinatorics

   
   

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Title
Optimizing quadratic forms of adjacency matrices of trees

Abstract
Let 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, 2002

Time
15:00

Room
Sala 5.5

 
     
 

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