Domination Number of Generalized Complements of a Graph

Let G be a graph with vertex set V. A set D ⊆ V is a dominating set of G if each vertex of V − D is adjacent to at least one vertex of D. The k (k(i))− complement of G is obtained by partitioning V into k partites and removing the edges between the vertices of different (same) partites in G and adding the edges between the vertices of different (same) partites which are not in G. This paper studies different domination numbers of k and k(i) complements of graphs.