2026-04-14T06:28:37Zhttps://recercat.cat/oai/requestoai:recercat.cat:10459.1/675122024-12-05T21:40:05Zcom_2072_3622col_2072_479130
RECERCAT
author
Dalfó, Cristina
author
Fiol Mora, Miguel Ángel
author
Sirán, Jozef
2024-12-05T21:40:05Z
2024-12-05T21:40:05Z
2019-11-11T12:14:53Z2020-01-02T23:12:31Z2019-01-022019-11-11T12:14:53Z
http://hdl.handle.net/10459.1/67512
We present a method to derive the complete spectrum of the lift Γα of a base digraph Γ , with voltage assignment α on a (finite) group G. The method is based on assigning to Γ a quotient-like matrix whose entries are elements of the group algebra C[G] , which fully represents Γα . This allows us to derive the eigenvectors and eigenvalues of the lift in terms of those of the base digraph and the irreducible characters of G. Thus, our main theorem generalizes some previous results of Lovász and Babai concerning the spectra of Cayley digraphs.The first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 734922. Research of the first two authors is supported by AGAUR under Project 2017SGR1087. The third author acknowledges support from the research Grants APVV 0136/12, APVV-15-0220, VEGA 1/0026/16, and VEGA 1/0142/17.
(c) Springer Science+Business Media, LLC, part of Springer Nature, 2019 info:eu-repo/semantics/openAccess
Digraph
Adjacency matrix
Regular partition
Quotient digraph
Spectrum
Lifted digraph
The spectra of lifted digraphs
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion