Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2603.29335 |
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Inhaltsangabe:
- 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.