2017/07/14 by C. Dalfó, Dalfó, C., M.A. Fiol +5
Engineering · Mathematics · #05C20 #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05C20 #msc:05C50 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1707.04463
arxiv created 2017/07/14 · openalex publication_date 2017/07/14 · arxiv updated 2017/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We present a method to derive the complete spectrum of the lift Γα of a base digraph Γ, with voltage assignments 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 generalize some previous results of Lováz and Babai concerning the spectra of Cayley digraphs.