Combined voltage assignments, factored lifts, and their spectra
Abstract
We consider lifting eigenvalues and eigenvectors of graphs to their factored lifts, derived by means of a combined voltage assignment in a group. The latter extends the concept of (ordinary) voltage assignments known from regular coverings and corresponds to the cases of generalized covers of Potocnik and Toledo (2021) in which a group of automorphisms of a lift acts freely on its arc set. With the help of group representations and certain matrices over complex group rings associated with the graphs to be lifted, we develop a method for the determination of the complete spectra of the factored lift graphs and derive a sufficient condition for lifting eigenvectors.
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