Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings

Abstract

Let ${\mathcal{G}}_R$ denote a unitary one-matching bi-Cayley graph over a finite commutative ring R. In this paper, we give a necessary and sufficient condition for ${\mathcal{G}}_R$ (respectively, the complement of ${\mathcal{G}}_R$ and the line graph of ${\mathcal{G}}_R$) to be Ramanujan.

Keywords:

• Unitary one-matching bi-Cayley graph
• spectrum
• Ramanujan

AMS Subject Classifications (2010):

• 05C50
• 05C25

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions, and also thank one of referees for raising Questions 5.2 and 5.3.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the National Natural Science Foundation of China (Nos. 12271439 and 11871398) and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (No. CX2020190).