Regular t-balanced Cayley maps on semi-dihedral groups

A Cayley map M = CM ( G , S , p ) is t-balanced if p ( x ) −1 = p t ( 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 ( 2 m + 1 )-balanced Cayley maps on semi-dihedral groups are constructed.