An algebraic approach to lifts of digraphs

Abstract

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, we completely determine the spectrum of . 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

The research of the first two authors have been partially supported by the Agency for Management of University and Research Grants of Catalonia (AGAUR) under project 2017SGR1087. The fifth author acknowledges support from the research grants APVV 0136/12, APVV-15-0220, VEGA 1/0026/16, and VEGA 1/0142/17. The first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.