On cospectral oriented graphs and cospectral signed graphs

Abstract

We consider oriented and also signed graphs which are cospectral, i.e. they are not switching isomorphic but share the same spectrum. We prove that there is a bijective correspondence between cospectral bipartite oriented graphs and cospectral bipartite signed graphs. We also give certain constructions of cospectral oriented (signed) graphs; for example, we provide infinite families of cospectral regular signed graphs and cospectral bipartite regular oriented graphs. In particular, we discuss relations between cospectral oriented graphs and cospectral signed graphs.