Combinatorial aspects of the nonsymmetric strong spectral property for graphs

Koljančić, Sara (avtor), Oblak, Polona (avtor)

In this paper, we investigate the nonsymmetric strong spectral property (nSSP) from a combinatorial perspective. To zero–nonzero patterns of matrices, we associate directed graphs and study when they require or allow the nSSP, providing a framework that avoids verifying the nSSP for individual matrices. A new combinatorial method is introduced and used to recognize several patterns that require the nSSP. It is shown that loop assignments in double paths play a critical role in establishing this property. In particular, we characterize all possible loop assignments for double paths on at most five vertices that require, allow or do not allow the nSSP, and show that an open question regarding irreducible tridiagonal patterns has a negative answer. We also investigate whether the minimum number of arcs in a directed graph on n vertices that requires the nSSP, is equal to 2n − 1, and confirm this minimum for several specific digraph families.

• Jezik: Angleški jezik
• Ključne besede: nonsymmetric strong spectral property, nSSP, sign pattern matrices, digraphs, inverse eigenvalue problem
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FRI - Fakulteta za računalništvo in informatiko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: Str. 755-779
• Številčenje: Vol. 42
• PID: 20.500.12556/RUL-190888
• UDK: 512.643:519.17
• ISSN pri članku: 1537-9582
• DOI: 10.13001/ela.2026.10523
• COBISS.SI-ID: 304180483
• Datum objave v RUL: 06.11.2026

Gradivo je del revije

• Naslov: The electronic journal of linear algebra
• Skrajšan naslov: Electron. j. linear algebra
• Založnik: International Linear Algebra Society
• ISSN: 1537-9582
• COBISS.SI-ID: 16372313

Licence

• Licenca: UND, Copyright Undetermined
• Povezava: http://rightsstatements.org/vocab/UND/1.0/
• Opis: Avtorskopravni status teh predmetov ni znan.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: nesimetrična krepka spektralna lastnost, nSSP, predznačeni vzorci matrik, usmerjeni grafi, inverzni problem lastnih vrednosti