The spectra of lifted digraphs
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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/67512 |
| Acceso en línea: | https://doi.org/10.1007/s10801-018-0862-y http://hdl.handle.net/10459.1/67512 |
| Access Level: | acceso abierto |
| Palabra clave: | Digraph Adjacency matrix Regular partition Quotient digraph Spectrum Lifted digraph |
| Sumario: | 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. |
|---|