Tetravalent one-regular graphs of order p2q2

Document Type : Original Article


Department of Mathematics, SRTT University


A graph is called one-regular if its full automorphism group acts regularly on the set of arcs. In this paper, we classify all connected one-regular graphs of valency 4 of order $p^2q^2$, where $p>q$ are prime numbers. We also prove that all such graphs are Cayley graphs.

Graphical Abstract

Tetravalent one-regular graphs of order p2q2

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Volume 8, Issue 2
July 2023
Pages 113-123
  • Receive Date: 01 June 2023
  • Revise Date: 06 June 2023
  • Accept Date: 12 June 2023
  • Publish Date: 01 July 2023