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arXiv · 2409.02463

Combined voltage assignments, factored lifts, and their spectra

C. Dalfó·M. A. Fiol·S. Pavlíková·J. Širáň
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Abstract

We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts}, derived by means of a {\em 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 Poto\v{c}nik 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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C. Dalfó, M. A. Fiol, S. Pavlíková, J. Širáň. 2024-09-04. Combined voltage assignments, factored lifts, and their spectra. https://arxiv.org/abs/2409.02463

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