M. Ghorbani - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, ۱۶۷۸۵-۱۳۶, I. R. Iran.
A. Seyyed-Hadi - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, ۱۶۷۸۵-۱۳۶, I. R. Iran.
F. Nowroozi-Larki - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, ۱۶۷۸۵-۱۳۶, I. R. Iran.

A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p> q$ are prime numbers.

symmetric graph, Cayley graph, normal graph, arc-transitive graph