A short proof of a perturbation inequality for the spectral radius
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910088301641728 |
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| author | Liu, Lele Ning, Bo |
| author_facet | Liu, Lele Ning, Bo |
| contents | Let $G$ be a simple graph, and denote by $λ(G)$ its spectral radius. Sun and Das (2020) established that for any non-isolated vertex $v$ with degree $d(v)$, \[ λ(G)\leq \sqrt{λ(G-v)^2 + 2d(v) - 1}, \] which is a conjecture original posed by Guo, Wang, and Li (2019). Sun and Das's proof uses several tools from spectral graph theory. In this short note, we provide a concise and self-contained proof of this inequality using matrix analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29335 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A short proof of a perturbation inequality for the spectral radius Liu, Lele Ning, Bo Combinatorics Let $G$ be a simple graph, and denote by $λ(G)$ its spectral radius. Sun and Das (2020) established that for any non-isolated vertex $v$ with degree $d(v)$, \[ λ(G)\leq \sqrt{λ(G-v)^2 + 2d(v) - 1}, \] which is a conjecture original posed by Guo, Wang, and Li (2019). Sun and Das's proof uses several tools from spectral graph theory. In this short note, we provide a concise and self-contained proof of this inequality using matrix analysis. |
| title | A short proof of a perturbation inequality for the spectral radius |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.29335 |