On cospectral oriented graphs and cospectral signed graphs

ABSTRACT

We consider oriented and also signed graphs which are cospectral, i.e. they are not switching isomorphic but share the same spectrum. We prove that there is a bijective correspondence between cospectral bipartite oriented graphs and cospectral bipartite signed graphs. We also give certain constructions of cospectral oriented (signed) graphs; for example, we provide infinite families of cospectral regular signed graphs and cospectral bipartite regular oriented graphs. In particular, we discuss relations between cospectral oriented graphs and cospectral signed graphs.

Keywords:

• Oriented graph
• signed graph
• eigenvalues
• bipartite graph
• regular graph

AMS CLASSIFICATIONS:

• 05C20
• 05C22
• 05C50

Acknowledgments

The author is grateful to the anonymous referees and the corresponding editor for some very valuable suggestions. In particular, a referee pointed the attention to the reference [4] that contains results that are closely related to certain results reported in this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Research is partially supported by Serbian Ministry of Education, Science and Technological Development via University of Belgrade.