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The spectra of lifted digraphs

Dalfó, C.; Fiol, M. A. and Širáň, J. (2019). The spectra of lifted digraphs. Journal of Algebraic Combinatorics, 50(4) pp. 419–426.

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We present a method to derive the complete spectrum of the lift \mathrm{\Gamma\alpha} of a base digraph \mathrm{\Gamma}, with voltage assignment α on a (finite) group $\textit{G}$. The method is based on assigning to \mathrm{\Gamma} a quotient-like matrix whose entries are elements of the group algebra \mathds{C}[$\textit{G}$], which fully represents \mathrm{\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 generalizes some previous results of Lovász and Babai concerning the spectra of Cayley digraphs.

Item Type: Journal Item
Copyright Holders: 2019 Springer Science+Business Media
ISSN: 1572-9192
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetAPVV 0136/12Not Set
Not SetAPVV-15-0220Not Set
Not SetVEGA 1/0026/16Not Set
Not SetVEGA 1/0142/17Not Set
Keywords: Digraph; Adjacency matrix; Regular partition; Quotient digraph; 10 Spectrum; Lifted digraph
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 58310
Depositing User: Jozef Širáň
Date Deposited: 14 Dec 2018 15:44
Last Modified: 04 Jul 2020 12:57
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