A short note on $A_α$-eigenvalues for simple graphs
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910000973086720 |
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| author | Barbarino, Giovanni |
| author_facet | Barbarino, Giovanni |
| contents | Given a simple graph $G$, its $A_α$ matrix is a convex combination with parameter $α\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds presented in [J. D. G. Silva Jr., C. S. Oliveira and L. M. G. C. Costa. "Some results involving the $A_α$-eigenvalues for graphs and line graphs"] for the spectral radius of $A_α$, and prove that one is better than the other when there are no isolated nodes in $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18365 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A short note on $A_α$-eigenvalues for simple graphs Barbarino, Giovanni Combinatorics Given a simple graph $G$, its $A_α$ matrix is a convex combination with parameter $α\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds presented in [J. D. G. Silva Jr., C. S. Oliveira and L. M. G. C. Costa. "Some results involving the $A_α$-eigenvalues for graphs and line graphs"] for the spectral radius of $A_α$, and prove that one is better than the other when there are no isolated nodes in $G$. |
| title | A short note on $A_α$-eigenvalues for simple graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.18365 |