Abstract
A Cayley graph constructed out of a group Γ and its generating set A is denoted by Cay (Γ, A). The digraph with the same node set as the original digraph is said to be a complement digraph if it has an edge from x to y exactly when the original digraph does not have an edge from x to y. A subset Ɖ of V is called a dominating set if each vertex in V- Ɖ is adjacent to at least one vertex in Ɖ. The minimum cardinality of a dominating set is called Domination number which is denoted by γ. The domination number of Cayley digraphs and Complement of Cayley digraphs of groups are investigated in this paper. Also, the graph relationship involving domination parameters in a graph and its complement are studied.
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