Hermitian adjacency matrices with at most three distinct eigenvalues
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909943913775104 |
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| author | Akbari, Saieed Aloni, Jonathan Levit, Maxwell Mohar, Bojan Xia, Steven |
| author_facet | Akbari, Saieed Aloni, Jonathan Levit, Maxwell Mohar, Bojan Xia, Steven |
| contents | We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct eigenvalues, showing that there are only four such graphs. We extend this result to mixed graphs. We show that there are infinitely many regular tournaments with three distinct eigenvalues. We extend our main results to Hermitian adjacency matrices defined over other roots of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hermitian adjacency matrices with at most three distinct eigenvalues Akbari, Saieed Aloni, Jonathan Levit, Maxwell Mohar, Bojan Xia, Steven Combinatorics We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct eigenvalues, showing that there are only four such graphs. We extend this result to mixed graphs. We show that there are infinitely many regular tournaments with three distinct eigenvalues. We extend our main results to Hermitian adjacency matrices defined over other roots of unity. |
| title | Hermitian adjacency matrices with at most three distinct eigenvalues |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.13781 |