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.



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.

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  • Item ORO ID
  • 58310
  • Item Type
  • Journal Item
  • 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 or School
  • Faculty of Science, Technology, Engineering and Mathematics (STEM)
  • Copyright Holders
  • © 2019 Springer Science+Business Media
  • Related URLs
  • Depositing User
  • Jozef Širáň