On the second largest adjacency eigenvalue of trees with given diameter
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910588292038656 |
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| author | Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng |
| author_facet | Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng |
| contents | For a graph $G$, let $λ_2(G)$ denote the second largest eigenvalue of the adjacency matrix of $G$. We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_2$ in the class $\mathcal{T}(n,d)$ of $n$-vertex trees with diameter $d$. This contributes to the literature on $λ_2$-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of $λ_2$ maximization over trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the second largest adjacency eigenvalue of trees with given diameter Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng Combinatorics 05C50 For a graph $G$, let $λ_2(G)$ denote the second largest eigenvalue of the adjacency matrix of $G$. We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_2$ in the class $\mathcal{T}(n,d)$ of $n$-vertex trees with diameter $d$. This contributes to the literature on $λ_2$-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of $λ_2$ maximization over trees. |
| title | On the second largest adjacency eigenvalue of trees with given diameter |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2409.01431 |