Cayley Graphs Of Small Valencies Of A Group Of Order 4p~2

A Cayley graph X = Cay(G, S) of group G is said to be normal if R(G), the group ofright multiplications, is normal in AutX. In this paper, by investigating the normality, weclassify 3-valent and 4-valent Cayley graphs of a group of order 4p², G = <a, b | a^p2 = b⁴ =1,a^b = a^r), where p＞3, r²=-1(modp²), p =1(mod4). In addition we obtain severalinfinite families of non-normal 4-valent Cayley graphs of a group of order 4p²,one of whichis one-regular graph.