The inverse eigenvalue problem of a graph: Multiplicities and minors

dc.contributor.author Barrett, Wayne
dc.contributor.author Butler, Steve
dc.contributor.author Hogben, Leslie
dc.contributor.author Fallat, Shaun
dc.contributor.author Hall, H. Tracy
dc.contributor.author Hogben, Leslie
dc.contributor.author Lin, Jephian
dc.contributor.author Shader, Bryan
dc.contributor.author Young, Michael
dc.contributor.department Mathematics
dc.date 2020-06-19T21:16:28.000
dc.date.accessioned 2020-06-30T06:00:19Z
dc.date.available 2020-06-30T06:00:19Z
dc.date.copyright Tue Jan 01 00:00:00 UTC 2019
dc.date.embargo 2021-10-31
dc.date.issued 2020-05-01
dc.description.abstract <p>The inverse eigenvalue problem of a given graph <em>G</em> is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in <em>G</em>. Barrett et al. introduced the Strong Spectral Property (SSP) and the Strong Multiplicity Property (SMP) in [Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph. <em>Electron. J. Combin.</em>, 2017]. In that paper it was shown that if a graph has a matrix with the SSP (or the SMP) then a supergraph has a matrix with the same spectrum (or ordered multiplicity list) augmented with simple eigenvalues if necessary, that is, subgraph monotonicity. In this paper we extend this to a form of minor monotonicity, with restrictions on where the new eigenvalues appear. These ideas are applied to solve the inverse eigenvalue problem for all graphs of order five, and to characterize forbidden minors of graphs having at most one multiple eigenvalue.</p>
dc.description.comments <p>This is a manuscript of an article published as Barrett, Wayne, Steve Butler, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Jephian C-H. Lin, Bryan L. Shader, and Michael Young. 142 "The inverse eigenvalue problem of a graph: Multiplicities and minors." <em>Journal of Combinatorial Theory, Series B</em> (2020): 276-306. DOI: <a href="https://doi.org/10.1016/j.jctb.2019.10.005" target="_blank">10.1016/j.jctb.2019.10.005</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/199/
dc.identifier.articleid 1212
dc.identifier.contextkey 14393119
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/199
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54588
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/199/2017_HogbenLeslie_InverseEigenvalue.pdf|||Fri Jan 14 22:01:00 UTC 2022
dc.source.uri 10.1016/j.jctb.2019.10.005
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords Inverse Eigenvalue Problem
dc.subject.keywords Strong Arnold Property
dc.subject.keywords Strong Spectral Property
dc.subject.keywords Strong Multiplicity Property
dc.subject.keywords Colin de Verdière type parameter
dc.subject.keywords Maximum multiplicity
dc.subject.keywords Distinct eigenvalues
dc.title The inverse eigenvalue problem of a graph: Multiplicities and minors
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 0131698a-00df-41ad-8919-35fb630b282b
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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