Distance and adjacency spectra and eigenspaces for three (di)graph lifts: A unified approach

Abstract

By the induced character theory, we first establish the irreducible decomposition of a permutation representation. Then, using it as a unified tool, we derive a decomposition formula for the distance spectrum and eigenspace of a regular lift of a graph, the adjacency spectra and eigenspaces of a relative lift and a ramified uniform lift of a digraph. The latter results are a complement of Dalfó et al. (2021) [6] and Deng et al. (2007) [8].