A sufficient condition for generalized spectral characterization of graphs with loops
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911463677886464 |
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| author | Van Werde, Alexander |
| author_facet | Van Werde, Alexander |
| contents | Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note establishes a related sufficient condition in the presence of loops: if the walk matrix has square-free determinant, then the graph is characterized by its generalized spectrum. The proof includes a general result about symmetric integral matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A sufficient condition for generalized spectral characterization of graphs with loops Van Werde, Alexander Combinatorics Number Theory Spectral Theory 05C50, 15B36, 11C20 Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note establishes a related sufficient condition in the presence of loops: if the walk matrix has square-free determinant, then the graph is characterized by its generalized spectrum. The proof includes a general result about symmetric integral matrices. |
| title | A sufficient condition for generalized spectral characterization of graphs with loops |
| topic | Combinatorics Number Theory Spectral Theory 05C50, 15B36, 11C20 |
| url | https://arxiv.org/abs/2511.19625 |