Subgroups as efficient dominating sets in Cayley graphs

Cayley graphs are graphs constructed out of a finite group ΓΓ and its generating set AA. Circulant graphs are Cayley graphs corresponding to finite cyclic groups. In this paper, the value of the domination number for some circulant graphs is obtained and a corresponding dominating set is also determined. At last a necessary and sufficient condition for a subgroup to be an efficient dominating set in circulant graphs is also obtained.