On symmetric spectra of Hermitian adjacency matrices for non-bipartite mixed graphs

We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for theta-Hermitian adjacency matrices defined by an angle theta is an element of (0, 7r]. We show that this equivalence holds when, for example, an angle theta is an algebraic number, while it breaks down for any angle theta is an element of (127r. Furthermore, we construct a family of non-bipartite mixed graphs having the symmetric spectra for given theta is an element of (127r. (c) 2024 Elsevier B.V. All rights reserved.