Abstract
Let Cay(S,A) denote a Cayley digraph of a semigroup S with a connection set A. A semigroup S is said to be a right group if it is isomorphic to the direct product of a group and a right zero semigroup and S is called a left group if it is isomorphic to the direct product of a group and a left zero semigroup. In this paper, we attempt to nd the value or bounds for the domination number of Cayley digraphs of right groups and left groups. Some examples which give sharpness of those bounds are also shown. Moreover, we consider the total domination number and give the necessary and sufficient conditions for the existence of total dominating sets in Cayley digraphs of right groups and left groups.
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