The minimum number of distinct eigenvalues of a threshold graph is at most $4$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912382082613248 |
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| author | Allem, Luiz Emilio Hoppen, Carlos Lazzarin, João Sibemberg, Lucas Siviero Tura, Fernando Colman |
| author_facet | Allem, Luiz Emilio Hoppen, Carlos Lazzarin, João Sibemberg, Lucas Siviero Tura, Fernando Colman |
| contents | In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most $4$. Moreover, given any threshold graph $G$ and any nonzero real number $λ$, we explicitly construct a matrix $M$ associated with $G$ such that DSpec$(M)\subseteq\{-λ,0,λ,2λ\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The minimum number of distinct eigenvalues of a threshold graph is at most $4$ Allem, Luiz Emilio Hoppen, Carlos Lazzarin, João Sibemberg, Lucas Siviero Tura, Fernando Colman Combinatorics In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most $4$. Moreover, given any threshold graph $G$ and any nonzero real number $λ$, we explicitly construct a matrix $M$ associated with $G$ such that DSpec$(M)\subseteq\{-λ,0,λ,2λ\}$. |
| title | The minimum number of distinct eigenvalues of a threshold graph is at most $4$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.13024 |