Normality Of4-valent Cayley Graphs Of Dihedral Group Of Order2_m

Let G be a finite group and S a subset of G such that1(?)S,|S|=4.A Cayley graph X=Cay(G,S) of group G is said to be normal if R(G),the group of right multiplications is normal in Aut(X).In this paper,by investigating their normality,we determine4-valent Cayley graphs of dihedral groups of order2m,G=<a,b|a2m-1=b2=1,ab=a-1),where m(>3)is a positive integer.In addition we obtain several infinite families of non-normal Cayley graphs of dihedral groups.