Cayley Graphs Of Small Valencies Of Quasi-dihedral Groups

Let G be a finite group and S a subset of G such that 1 (?) S.The Cayley digraph Cay(G,S) on G with respect to S is defined to have vertex set V(Cay(G, S)) = G and edge set E(Cay(G, S)) = {(g,sg) | g∈G,s∈S}. If S^-1 = S then Cay (G,S) ,called a Cayley graph , is viewed as an undirected graph by identifying two oppositely directed edges with one undirected edge .It is seen that a Cayley digraph Cay(G, S) is connected if and only if S generates G,and Aut(G,S) = {α∈Aut(G) | S^α= S) is a subgroup of the automorphism group Aut(Cay(G, S)) of Cay(G, S). 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 quasi-dihedral groups of order Am, G = 2m = b² = 1, a^b = a^m+1>, where m = 2^Ï„,r > 2. In addition we obtain several infinite families of normal Cayley graphs of Quasi-dihedral groups.