Nut graphs with a given automorphism group
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910436778049536 |
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| author | Bašić, Nino Fowler, Patrick W. |
| author_facet | Bašić, Nino Fowler, Patrick W. |
| contents | A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nut graphs with a given automorphism group Bašić, Nino Fowler, Patrick W. Combinatorics 05C25, 05C50 A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly. |
| title | Nut graphs with a given automorphism group |
| topic | Combinatorics 05C25, 05C50 |
| url | https://arxiv.org/abs/2405.04117 |