Mixed graphs with H-rank 3

In the article (Mohar, 2016 [9]), Mohar determined all mixed graphs with H-rank 2, and used it to classify cospectral graphs with respect to their Hermitian adjacency matrix, constructing a class of graphs which can not be determined by their H-spectrum. In the present paper, we investigate the H-rank of mixed graphs further, determining the H-ranks of those mixed graphs with trees, cycles and complete bipartite graphs as underlying graphs, respectively. Moreover, we characterize all mixed graphs with H-rank 3, and show that all connected mixed graphs with H-rank 3 can be determined by their H-spectrum.