A note on the singularity of oriented graphs

An oriented graph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. In this note, by a new approach, we determine the singularity of oriented quasi-trees. The main results of Chen et al. ['Singularity of oriented graphs from several classes', Bull. Aust. Math. Soc. 102(1) (2020), 7-14] follow as corollaries. Furthermore, we give a necessary condition for an oriented bipartite graph to be nonsingular. By applying this condition, we characterise nonsingular oriented bipartite graphs B-m,B-n when min{m, n} <= 3.