Switching methods of level 2 for the construction of cospectral graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918473144205312 |
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| author | Abiad, Aida van de Berg, Nils Simoens, Robin |
| author_facet | Abiad, Aida van de Berg, Nils Simoens, Robin |
| contents | A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed using regular orthogonal matrices of level 2, which has relevance for Haemers' conjecture. We present two new switching methods and several combinatorial and geometrical reformulations of existing switching operations of level 2. We also introduce the concept of reducibility and use it to classify all irreducible switching methods that correspond to a conjugation with a regular orthogonal matrix of level 2 with one nontrivial indecomposable block, up to switching sets of size 12, extending previous results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Switching methods of level 2 for the construction of cospectral graphs Abiad, Aida van de Berg, Nils Simoens, Robin Combinatorics 05C50 A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed using regular orthogonal matrices of level 2, which has relevance for Haemers' conjecture. We present two new switching methods and several combinatorial and geometrical reformulations of existing switching operations of level 2. We also introduce the concept of reducibility and use it to classify all irreducible switching methods that correspond to a conjugation with a regular orthogonal matrix of level 2 with one nontrivial indecomposable block, up to switching sets of size 12, extending previous results. |
| title | Switching methods of level 2 for the construction of cospectral graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2410.07948 |