Combinatorial aspects of the non-symmetric strong spectral property for graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913057798619136 |
|---|---|
| author | Koljančić, Sara Oblak, Polona |
| author_facet | Koljančić, Sara Oblak, Polona |
| contents | In this paper, we investigate the non-symmetric 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 recognise several patterns that require the nSSP. It is shown that loop assignments in double paths play a critical role in establishing this property, and we 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21552 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial aspects of the non-symmetric strong spectral property for graphs Koljančić, Sara Oblak, Polona Combinatorics Spectral Theory 05C50, 05C38, 15B35, 15A29 In this paper, we investigate the non-symmetric 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 recognise several patterns that require the nSSP. It is shown that loop assignments in double paths play a critical role in establishing this property, and we 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. |
| title | Combinatorial aspects of the non-symmetric strong spectral property for graphs |
| topic | Combinatorics Spectral Theory 05C50, 05C38, 15B35, 15A29 |
| url | https://arxiv.org/abs/2604.21552 |