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

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

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.

• Language: English
• Keywords: inverse eigenvalue problem, minimum number of distinct eigenvalues, borderings, joins of graphs, paths, cycles, hypercubes
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science ; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 104-126
• Numbering: Vol. 679
• PID: 20.500.12556/RUL-150996
• UDC: 519.17
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2023.09.013
• COBISS.SI-ID: 165826307
• Publication date in RUL: 26.09.2023

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: North Holland
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: inverzni problem lastnih vrednosti, najmanjše število različnih lastnih vrednosti, ograjevanje, spoj grafov, poti, cikli, hiperkocke