Characterizing graphs with the second largest distance eigenvalue less than -1/2
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912899092447232 |
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| author | Abdón, Miriam Markenzon, Lilian Vinagre, Cybele T. M. |
| author_facet | Abdón, Miriam Markenzon, Lilian Vinagre, Cybele T. M. |
| contents | Let $G$ be a connected graph with vertex set $V$. The distance, $d_G(u, v)$, between vertices $u$ and $v$ of $G$ is defined as the length of a shortest path between $u$ and $v$ in $G$. The distance matrix of $G$ is the matrix $\mathbf{D}(G) =[d_G(u, v)]_{u,v\in V}$. The second largest distance eigenvalue $λ_2(G)$ of $G$ is the second largest one in the spectrum of $\mathbf{D}(G)$.
In this work, we completely characterize the connected graphs $G$ for which $λ_2(G)<-1/2$ through approaches both spectral and structural. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11331 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizing graphs with the second largest distance eigenvalue less than -1/2 Abdón, Miriam Markenzon, Lilian Vinagre, Cybele T. M. Combinatorics 05C50, 05C75 Let $G$ be a connected graph with vertex set $V$. The distance, $d_G(u, v)$, between vertices $u$ and $v$ of $G$ is defined as the length of a shortest path between $u$ and $v$ in $G$. The distance matrix of $G$ is the matrix $\mathbf{D}(G) =[d_G(u, v)]_{u,v\in V}$. The second largest distance eigenvalue $λ_2(G)$ of $G$ is the second largest one in the spectrum of $\mathbf{D}(G)$. In this work, we completely characterize the connected graphs $G$ for which $λ_2(G)<-1/2$ through approaches both spectral and structural. |
| title | Characterizing graphs with the second largest distance eigenvalue less than -1/2 |
| topic | Combinatorics 05C50, 05C75 |
| url | https://arxiv.org/abs/2602.11331 |