Combined voltage assignments, factored lifts, and their spectra
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929485942620160 |
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| author | Dalfó, C. Fiol, M. A. Pavlíková, S. Širáň, J. |
| author_facet | Dalfó, C. Fiol, M. A. Pavlíková, S. Širáň, J. |
| contents | We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts}, derived by means of a {\em combined voltage assignment} in a group. The latter extends the concept of (ordinary) voltage assignments known from regular coverings and corresponds to the cases of generalized covers of Potočnik and Toledo (2021) in which a group of automorphisms of a lift acts freely on its arc set. With the help of group representations and certain matrices over complex group rings associated with the graphs to be lifted, we develop a method for the determination of the complete spectra of the factored lift graphs and derive a sufficient condition for lifting eigenvectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combined voltage assignments, factored lifts, and their spectra Dalfó, C. Fiol, M. A. Pavlíková, S. Širáň, J. Combinatorics We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts}, derived by means of a {\em combined voltage assignment} in a group. The latter extends the concept of (ordinary) voltage assignments known from regular coverings and corresponds to the cases of generalized covers of Potočnik and Toledo (2021) in which a group of automorphisms of a lift acts freely on its arc set. With the help of group representations and certain matrices over complex group rings associated with the graphs to be lifted, we develop a method for the determination of the complete spectra of the factored lift graphs and derive a sufficient condition for lifting eigenvectors. |
| title | Combined voltage assignments, factored lifts, and their spectra |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.02463 |