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SINGULARITY OF ORIENTED GRAPHS FROM SEVERAL CLASSES

Part of: Graph theory

Published online by Cambridge University Press:  21 November 2019

XIAOXUAN CHEN Open the ORCID record for XIAOXUAN CHEN [Opens in a new window] ,
JING YANG Open the ORCID record for JING YANG [Opens in a new window] ,
XIANYA GENG Open the ORCID record for XIANYA GENG [Opens in a new window]  and
LONG WANG Open the ORCID record for LONG WANG [Opens in a new window]
XIAOXUAN CHEN
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China email 765834082@qq.com
JING YANG*
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China email jyang@aust.edu.cn
XIANYA GENG
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China email gengxianya@sina.com
LONG WANG
Affiliation:
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China email wanglongxuzhou@126.com
*
✉jyang@aust.edu.cn
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Abstract

A digraph is called oriented if there is at most one arc between two distinct vertices. An oriented graph $D$ is nonsingular if its adjacency matrix $A(D)$ is nonsingular. We characterise all nonsingular oriented graphs from three classes: graphs in which cycles are vertex disjoint, graphs in which all cycles share exactly one common vertex and graphs formed by cycles sharing a common path. As a straightforward corollary, the singularity of oriented bicyclic graphs is determined.

Keywords

oriented graphsingularityrank

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 7 - 14
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

Supported by National Natural Science Foundation of China (61702008, 11701008), Natural Science Foundation of Anhui Province (1808085MF193, 1808085QA04, 1908085QA31), Educational Commission of Anhui Province of China (KJ2018A0081) and Research Program of Outstanding Young Backbone Talents in Colleges and Universities of Anhui Province (GXGWFX2019015).

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