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The spectra of lifted digraphs | | C. Dalfó
; M. A. Fiol
; J. Širáň
; | | Date: |
14 Jul 2017 | | Abstract: | We present a method to derive the complete spectrum of the lift
$Gamma^alpha$ of a base digraph $Gamma$, with voltage assignments on a
(finite) group $G$. The method is based on assigning to $Gamma$ a
quotient-like matrix whose entries are elements of the group algebra
$mathbb{C}[G]$, which fully represents $Gamma^{alpha}$. 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 Lov’az and Babai concerning the spectra of
Cayley digraphs. | | Source: | arXiv, 1707.4463 | | Services: | Forum | Review | PDF | Favorites | |
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