Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs

Aida Abiad, Shaun M. Fallat, Mark Kempton, Rupert H. Levene, Polona Oblak (Corresponding author), Helena Šmigoc, Michael Tait, Kevin N. Vander Meulen

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Samenvatting

An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on bordering a matrix and attempt to control the change in the number of distinct eigenvalues induced by this operation. By applying bordering techniques to the join of graphs, we obtain numerous results on the nature of the minimum number of distinct eigenvalues as vertices are joined to a fixed graph.

Originele taal-2Engels
Pagina's (van-tot)104-126
Aantal pagina's23
TijdschriftLinear Algebra and Its Applications
Volume679
DOI's
StatusGepubliceerd - 15 dec. 2023

Financiering

Partially supported by the Research Foundation Flanders (FWO) grant 1285921N.Research supported in part by an NSERC Discovery Grant RGPIN–2019–03934.Partially supported by Slovenian Research Agency (research core funding no. P1-0222 and project no. J1-3004).Partially supported by National Science Foundation grant DMS-2011553 and a Villanova University Summer Grant.Research supported in part by an NSERC Discovery Grant RGPIN–2022–05137.This project started and was made possible by the online research community Inverse eigenvalue problems for graphs, which is sponsored by the American Institute of Mathematics with support from the US National Science Foundation. The authors thank AIM and the research community organizers for their support. We are grateful to the anonymous referee for careful reading and comments, which improved the presentation of the paper. This project started and was made possible by the online research community Inverse eigenvalue problems for graphs, which is sponsored by the American Institute of Mathematics with support from the US National Science Foundation . The authors thank AIM and the research community organizers for their support.

FinanciersFinanciernummer
National Science Foundation(NSF)DMS-2011553
American Institute of Mathematics
Villanova UniversityRGPIN–2022–05137
Natural Sciences and Engineering Research Council of CanadaRGPIN–2019–03934
Fonds Wetenschappelijk Onderzoek1285921N

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