Daisy P. Salve, Enrico L. Enriquez
Let G be a connected simple graph. A dominating set S ⊆ V (G) is called a perfect dominating set of G if each u ∈ V (G)\S is dominated by exactly one element of S. The perfect domination number of G, denoted by γp(G), is the minimum cardinality of a perfect dominating set of G. Let D be a minimum perfect dominating set of G. A perfect dominating set S ⊆ (V (G)\D) is called an inverse perfect dominating set of G with respect to D. The inverse perfect domination number of G denoted by γ−1p (G) is the minimum cardinality of an inverse perfect dominating set of G. An inverse perfect dominating set of cardinality γ−1p (G) is called γ−1p -set. In this paper, we show that every integers k and n with 1 ≤ k < n is realizable as inverse perfect domination number and order of G respectively. Further, we give the characterization of the inverse perfect dominating set with inverse perfect 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
