Teodora J. Punzalan, Enrico L. Enriquez
Let G be a connected simple graph. A set S ⊆ V (G) is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V (G)\S. Let D be a minimum restrained dominating set in G. A restrained dominating set S ⊆ (V (G) \D) is called an inverse restrained dominating set of G with respect to D. The inverse restrained domination number ofGdenoted by γr−1 (G) is the minimum cardinality of an inverse restrained dominating set of G. An inverse restrained dominating set of cardinality γr−1 (G) is called γr−1 -set. In this paper, we show that every integers k and n with 1 ≤ k < nis realizable as inverse restrained domination number and order of G respectively. Further, we give the characterization of the inverse restrained dominating set with inverse restrained domination numbers of one and two and give some important results. © Research India Publications.
Department of Mathematics, School of Arts and Sciences, University of San Carlos, Cebu City, 6000, Philippines
