Cayley Graphs Of Small Valencies Of Semi-dihedral Groups

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 AutX. In this paper, by investigating the nomality, we classify 3-valent and 4-valent Cayley graphs of semi-dihedral groups of order 4m, G = (a,b | a^2m = b² = 1,a⁶ = a^m-1), where m = 2^r,r > 2. In addition we obtain several infinite families of non-normal Cayley graphs of semi-dihedral groups.