Constructing cospectral graphs via regular rational orthogonal matrix with level two and three
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910605198229504 |
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| author | Mao, Lihuan Yan, Fu |
| author_facet | Mao, Lihuan Yan, Fu |
| contents | Two graphs $G$ and $H$ are \emph{cospectral} if the adjacency matrices share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature, e.g. the famous GM-switching method. In this paper, we shall construct cospectral graphs via regular rational orthogonal matrix $Q$ with level two and three. We provide two straightforward algorithms to characterize with adjacency matrix $A$ of graph $G$ such that $Q^TAQ$ is again a (0,1)-matrix, and introduce two new switching methods to construct families of cospectral graphs which generalized the GM-switching to some extent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing cospectral graphs via regular rational orthogonal matrix with level two and three Mao, Lihuan Yan, Fu Combinatorics Spectral Theory 05C50 Two graphs $G$ and $H$ are \emph{cospectral} if the adjacency matrices share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature, e.g. the famous GM-switching method. In this paper, we shall construct cospectral graphs via regular rational orthogonal matrix $Q$ with level two and three. We provide two straightforward algorithms to characterize with adjacency matrix $A$ of graph $G$ such that $Q^TAQ$ is again a (0,1)-matrix, and introduce two new switching methods to construct families of cospectral graphs which generalized the GM-switching to some extent. |
| title | Constructing cospectral graphs via regular rational orthogonal matrix with level two and three |
| topic | Combinatorics Spectral Theory 05C50 |
| url | https://arxiv.org/abs/2409.09998 |