Orthogonalisability of joins of graphs

Levene, Rupert H. (author), Oblak, Polona (author), Šmigoc, Helena (author)

A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the connected components of two graphs for their join to be orthogonalisable. In some cases, those conditions coincide, and we present several families of joins of graphs that are orthogonalisable.

• Language: English
• Keywords: symmetric matrix, orthogonal matrix, inverse eigenvalue problem, minimum number of distinct eigenvalues, join of graphs
• 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: 2025
• Number of pages: Str. 162-181
• Numbering: Vol. 723
• PID: 20.500.12556/RUL-169919
• UDC: 519.17
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2025.06.001
• COBISS.SI-ID: 239398147
• Publication date in RUL: 16.06.2025

Record is a part of a journal

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

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

• Language: Slovenian
• Keywords: simetrična matrika, ortogonalna matrika, najmanjše število različnih lastnih vrednosti, spoj grafov, inverzni problem lastnih vrednosti

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika