Cubic graphs with no eigenvalues in the interval (-1,1)
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917768287223808 |
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| author | Guo, Krystal Royle, Gordon F. |
| author_facet | Guo, Krystal Royle, Gordon F. |
| contents | We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval $(-1,1)$. There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Kollár and Sarnak [Communications of the AMS. 1,1--38], and $14$ "sporadic" graphs on at most $32$ vertices. This allows us to show that $(-1,1)$ is a maximal spectral gap set for cubic graphs. Our techniques including examination of various substructure and an application of the classification of generalized line graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cubic graphs with no eigenvalues in the interval (-1,1) Guo, Krystal Royle, Gordon F. Combinatorics 2020: Primary 05C50, Secondary 05C76 We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval $(-1,1)$. There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Kollár and Sarnak [Communications of the AMS. 1,1--38], and $14$ "sporadic" graphs on at most $32$ vertices. This allows us to show that $(-1,1)$ is a maximal spectral gap set for cubic graphs. Our techniques including examination of various substructure and an application of the classification of generalized line graphs. |
| title | Cubic graphs with no eigenvalues in the interval (-1,1) |
| topic | Combinatorics 2020: Primary 05C50, Secondary 05C76 |
| url | https://arxiv.org/abs/2409.02678 |