1. A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS.
- Author
-
MA, XIAOBIN and JIANG, FAN
- Subjects
- *
DIRECTED graphs , *BIPARTITE graphs , *MATHEMATICS - 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 $\min \{m,n\}\leq 3$. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF