4-valent Cayley Graphs Of Group Of Order 2pq

Let G be a finite group and T a generating subset of G such that 1(?)T.A Cayley graph X = Cay(G,T)of group G is said to be normal if R(G),the group of right.multiplications is normal in full automorphism group Aut(X)=Aut(Cay(G,T)).Let G =<a,b|apq=b2=1,ab=ar>,where r2?1(mod pq),where p,p is a prime,p>3,q>3.In this paper,we determine the normality of any 4-valent Cayley graph of G,and show that any 4-valent Cayley graph of G is normal.As a result,we obtain a kind of 4-valent one-regular Cayley graph.