An algebraic approach to lifts of digraphs

Dalfó, C.; Fiol, M. A.; Miller, M.; Ryan, J. and Širáň, J. (2019). An algebraic approach to lifts of digraphs. Discrete Applied Mathematics, 269 pp. 68–76.

DOI: https://doi.org/10.1016/j.dam.2018.10.040

Abstract

We present some applications of a new matrix approach for studying the properties of the lift $\Gamma^{\alpha}$ of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, we completely determine the spectrum of $\Gamma^{\alpha}$. As some examples of our technique, we study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman–Singleton graph.

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