On prime-valent symmetric graphs of order four times an odd prime power

Abstract

In this paper, we classify symmetric basic prime-valent graphs of order four times an odd prime power. As an application, prime-valent symmetric graphs of order four times a prime or prime square are specifically determined. We remark that special cases for valency 5 and 7 were characterized by Yang etc. (Eur. J. Combin. 80:236–246, 2019) and Pan and Yin (J. Algebr. Appl. 17(5):1850093, 2018).

Keywords:

• Symmetric graph
• normal quotient graph
• normal cover

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20B15
• 20B30
• 05C25

Acknowledgements

The authors are very grateful to the referee for the valuable comments.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China (11961076).