On the minimum number of eigenvalues of matrices associated with cographs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915781541888000 |
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| author | Allem, Luiz Emilio Fürer, Martin Hoppen, Carlos Sibemberg, Lucas Siviero Trevisan, Vilmar |
| author_facet | Allem, Luiz Emilio Fürer, Martin Hoppen, Carlos Sibemberg, Lucas Siviero Trevisan, Vilmar |
| contents | A symmetric matrix $M=(m_{ij}) \in \mathbb{R}^{n \times n}$ is said to be associated with an $n$-vertex graph $G=(V,E)$ with vertex set $\{v_1,\ldots,v_n\}$ if, for every $i \neq j$, we have $m_{ij} \neq 0$ if and only if $\{v_i,v_j\}\in E$. We prove that, for every cograph $G$, there is a matrix $M$ associated with $G$ for which the number of distinct eigenvalues is at most 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07282 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the minimum number of eigenvalues of matrices associated with cographs Allem, Luiz Emilio Fürer, Martin Hoppen, Carlos Sibemberg, Lucas Siviero Trevisan, Vilmar Combinatorics 05C50 A symmetric matrix $M=(m_{ij}) \in \mathbb{R}^{n \times n}$ is said to be associated with an $n$-vertex graph $G=(V,E)$ with vertex set $\{v_1,\ldots,v_n\}$ if, for every $i \neq j$, we have $m_{ij} \neq 0$ if and only if $\{v_i,v_j\}\in E$. We prove that, for every cograph $G$, there is a matrix $M$ associated with $G$ for which the number of distinct eigenvalues is at most 4. |
| title | On the minimum number of eigenvalues of matrices associated with cographs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2602.07282 |