| 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|a8p2 = b2=1,ab =ar). where r = 1 - 2p2, where p is a prime, p > 7. 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 two kinds of 4-valent one-regular Cayley graphs. |
