Spectra of signed graphs and related oriented graphs

Abstract

For every oriented graph G′, there exists a bipartite signed graph Ḣ such that the spectrum of Ḣ contains the full information about the spectrum of the skew adjacency matrix of G′. This allows us to transfer some problems concerning the skew eigenvalues of oriented graphs to the framework of signed graphs, where the theory of real symmetric matrices can be employed. In this paper, we continue the previous research by relating the characteristic polynomials, eigenspaces and the energy of G′ to those of Ḣ. Simultaneously, we address some open problems concerning the skew eigenvalues of oriented graphs.