@inbook{f39544f44df1408aa444f9ac3742edf7,

title = "Eigenvalues, multiplicities and graphs",

abstract = "For a given graph, there is a natural question of the possible lists of multiplicities for the eigenvalues among the spectra of Hermitian matrices with that graph (no constraint is placed upon the diagonal entries of the matrices by the graph). Here, we survey some of what is known about this question and include some new information about it. There is a natural focus upon the case in which the graph is a tree. In this event, there is remarkable structure to the possible lists. Both the general theory and a summary of specific results is given. At the end, this allows to give, in compact tabular form, all lists for trees on fewer than 11 vertices (a potentially valuable tool for further work). There is a brief discussion of non-trees.",

keywords = "Eigenvalue, Graph, Hermitian matrix, Multiplicities, Parter vertex, Symmetric matrix, Tree",

author = "Johnson, {Charles R.} and Ant{\'o}nio Leal-Duarte and Saiago, {Carlos Manuel} and Sher, {David A.}",

note = "Sem PDF conforme despacho.",

year = "2006",

doi = "10.1090/conm/419/08003",

language = "English",

isbn = "978-0-8218-3842-6",

volume = "419",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

number = "419",

pages = "167--183",

editor = "Huynh, {Dinh V.} and Jain, {S. K.} and L{\'o}pez-Permouth, {S. R.}",

booktitle = "Algebra and Its Applications",

}