A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS. Issue 3 (25th December 2022)

• Record Type: Journal Article
• Authors: MA, XIAOBIN; JIANG, FAN
• Is Part Of: Bulletin of the Australian Mathematical Society. Volume 106:Issue 3(2022)
• Page Start: 357
• Page End: 362
• Publication Date: 2022-12-25
• Subjects: 05C50; singularity -- oriented graph -- adjacency matrix; Mathematics -- Societies, etc; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S000497272200034X
• Languages: English
• ISSNs: 0004-9727

Abstract

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 $\min \{m, n\}\leq 3$ .