The spectra of lifted digraphs
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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.
Is part ofJournal of Algebraic Combinatorics, 2019, vol. 50, núm. 4, p. 419-426
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Dalfó, Cristina; Fiol, Miguel Angel (Elsevier, 2020)In this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on n letters. We prove that every partition of the ...
Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe; Sirán, Josef (Elsevier, 2018)We present some applications of a new matrix approach for studying the properties of the lift of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, ...
Dalfó, Cristina; Fiol, Miguel Angel; Pavlíková, Sona; Sirán, Josef (Faculty of Mathematics, Physics and Informatics, Comenius University, 2019)We describe, in a very explicit way, a method for determining the spec-tra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regularor not).