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A NOTE ON THE SINGULARITY OF ORIENTED GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  25 April 2022

XIAOBIN MA Open the ORCID record for XIAOBIN MA [Opens in a new window]  and
FAN JIANG Open the ORCID record for FAN JIANG [Opens in a new window]
XIAOBIN MA*
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, PR China
FAN JIANG
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, PR China e-mail: 1686951558@qq.com
*
e-mail: maxiaobinzaozhuang@163.com
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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 $\min \{m,n\}\leq 3$ .

Keywords

singularityoriented graphadjacency matrix

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 357 - 362
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Supported by National Natural Science Foundation of China (12001010), Natural Science Foundation of Anhui Province (1908085QA31), China Postdoctoral Foundation (2019M662131).

References

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