Acyclic matrices with a small number of distinct eigenvalues

Abstract

Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible. © 2011 Elsevier Inc. All rights reserved.