Homomorphisms, representations and characteristic polynomials of digraphs

AbstractThe existence of a homomorphism between two digraphs often implies many structural properties. We collect in this paper some characterizations of various digraph homomorphisms using matrix equations and fiber partitions. We also survey the relationship among the characteristic polynomials of a digraph and its divisors. This includes an introduction of the concept of branched coverings of digraphs, their voltage assignment representations, and a decomposition formula for the characteristic polynomial of a branched cover with branch index 1. Some open problems are included

On automorphisms of circulant digraphs on pm vertices, p an odd prime

AbstractThe circulant digraph Γ is considered when the number n of vertices of Γ is equal to pm for an odd prime p. The main results are an implicit characterization of the groups Aut(Γ) in the general case, and an explicit characterization in the case n=p4. The argument is based on spectral techniques and classical constructions of permutation groups