On cospectral signed digraphs

Abstract

The set of distinct eigenvalues of a signed digraph \(S\) together with their respective multiplicities is called its spectrum. Two signed digraphs of same order are said to be cospectral if they have the same spectrum. In this paper, we show the existence of integral, real and Gaussian cospectral signed digraphs. We give a spectral characterization of normal signed digraphs and use it to construct cospectral normal signed digraphs.