A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS. Issue 3 (25th December 2022) - MA, XIAOBIN; JIANG, FAN
Abstract: 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 $B_{m, n}$ when $\min \{m, n\}≤ 3$ .