The strong spectral property for some families of unicyclic graphs

Koljančić, Sara (author), Oblak, Polona (author)

To find all the possible spectra of all real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of a given graph G, the Strong Spectral Property turns out to be of crucial importance. In particular, we investigate the set $\mathcal{G}$$^{SSP}$ of all simple graphs G with the property that each symmetric matrix of the pattern of G has the Strong Spectral Property. In this paper, we completely characterize unicyclic graphs of girth three in $\mathcal{G}$$^{SSP}$. We prove that any tadpole graph of girth at most five is in $\mathcal{G}$$^{SSP}$ and we show that the same is not valid for girth six tadpole graphs.

• Language: English
• Keywords: symmetric matrix, strong spectral property, inverse eigenvalue problem
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Year: 2027
• Number of pages: Str. 151-174
• Numbering: Vol. 754
• PID: 20.500.12556/RUL-190439
• UDC: 519.17:512.643
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2026.10.023
• COBISS.SI-ID: 302420995
• Publication date in RUL: 29.10.2026

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 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: simetrična matrika, krepka spektralna lastnost, inverzni problem lastnih vrednosti