Document Type: Original Manuscript
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, 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.