Normality Of Cayley Graphs Of One Class Of Groups Of Order 8p~2

Let G be a finite group and T a generated subset of group G that does not con-tain identity 1.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 the full automorphism group Aut(X)=Aut(Cay(G,T)).The group G discussed in this paper is a wreath product of Z2p by Z2,that is G=(<a>×<c>):(b),o(a)=o(c)=2p,o(b)=2,[a,c]=1,a6=c,c6=a,p>3,where p is a prime.By studying the 3-valent Cayley graphs of group G,we prove that any 3-valent Cayley graph of group G is non-normal,and can be divided into two classes up to graph isomorphism whose stabilizers are isomorphisc to Z2 × Z2 and S3,respectively.Moreover,the 3-valent connected Cayley graph of G with vertex stabi-lizer S3 is a class of non-normal 2-regular graphs.At the same time,we also obtain some new 4-valent connected non-normal Cayley graphs and GRR by studying the 4-valent Cayley graphs of group G.