Regular t-balanced Cayley maps on semi-dihedral groups

A Cayley map M=CM(G,S,p) is t-balanced if p−1(x)=pt(x−1) for every x∈S. In this paper, we classify the regular t-balanced Cayley maps on semi-dihedral groups for any t. As a result, for every positive integer m, 4m-valent regular (2m+1)-balanced Cayley maps on semi-dihedral groups are constructed.