Inverse Fair Restrained Domination in the Corona of Two Graphs
Villa S. Verdad, Enrico L. Enriquez Β· International Journal of Mathematics Trends and Technology Β· 2023
Let πΊ be a connected simple graph. A dominating subset S of π(πΊ) is a fair dominating set in πΊ if all the vertices not in π are dominated by the same number of vertices from π. A fair dominating set π β π(πΊ) is a fair restrained dominating set if every vertex not in π is adjacent to a vertex in π and to a vertex in π(πΊ) β π. Alternately, a fair dominating set π β π(πΊ) is a fair restrained dominating set if π[π] = π(πΊ) and β©π(πΊ) β πβͺ is a subgraph without isolated vertices. Let π· be a minimum fair restrained dominating set of πΊ. A fair restrained dominating set π β (π(πΊ) β π·) is called an inverse fair restrained dominating set of G with respect to π·. The inverse fair restrained domination number of πΊ denoted by πΎπππ β1 (πΊ) is the minimum cardinality of an inverse fair restrained dominating set of πΊ. An inverse fair restrained dominating set of cardinality πΎπππ β1 (πΊ) is called πΎπππ β1 (πΊ)-set. In this paper, the researchers investigate the concept and give some important results on inverse fair restrained dominating sets under the corona of two graphs.