Limit points of $A_α$-matrices of graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911843393470464 |
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| author | Oliveira, Elismar R. Trevisan, Vilmar |
| author_facet | Oliveira, Elismar R. Trevisan, Vilmar |
| contents | We study limit points of the spectral radii of $A_α$-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of $A_α$-limit points of caterpillars for $α$ close to zero. Precisely, we show that for $α\in [0, 1/2)$ there exists a positive number $τ_2(α)>2$ such that any value $λ> τ_2(α)$ is an $A_α$-limit point. We also determine the existence of other intervals for which all its points are $A_α$-limit points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit points of $A_α$-matrices of graphs Oliveira, Elismar R. Trevisan, Vilmar Combinatorics Spectral Theory 05C50, 05C05, 15A18 We study limit points of the spectral radii of $A_α$-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of $A_α$-limit points of caterpillars for $α$ close to zero. Precisely, we show that for $α\in [0, 1/2)$ there exists a positive number $τ_2(α)>2$ such that any value $λ> τ_2(α)$ is an $A_α$-limit point. We also determine the existence of other intervals for which all its points are $A_α$-limit points. |
| title | Limit points of $A_α$-matrices of graphs |
| topic | Combinatorics Spectral Theory 05C50, 05C05, 15A18 |
| url | https://arxiv.org/abs/2404.10953 |