Eigenvalues of oriented-graph matrices Original Research Article

We give bounds on the real and imaginary parts of the eigenvalues of an oriented-graph matrix, prove that each of the irreducible oriented-graph matrices of order n ≥ 3 has at least three distinct eigenvalues, and determine such irreducible matrices with three distinct eigenvalues. We also consider spectral properties of the bipartite oriented-graph matrices and the multiequipartite oriented-graph matrices.