Modjtaba Ghorbani
Aziz SeyyedHadi - Department of Mathematics, SRTT University
Farzaneh Nowroozi-Larki - 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 ۴ of order p^۲q^۲, where p>q are prime numbers. We also prove that all such graphs are Cayley graphs.