Proponent/Claimant
Abstract
Let πΊ = (π(πΊ),πΈ(πΊ)) be a connected simple graph. A subset π of π(πΊ) is a dominating set of πΊ if for every π’ β π(πΊ\π), there exists π£ β π such that π’π£ β πΈ(πΊ). A dominating set π· is called a restrained dominating set if for each π’ β π(πΊ)\π· there exist π£ β π(π·) and π§ β π(πΊ)\π·(π§ β π’) such that π’ is adjacent to π£ and π§. Further, if π· is a minimum restrained dominating set of πΊ, then a restrained dominating set π β π(πΊ)\π· is called an inverse restrained dominating set of πΊ with respect to π·. A disjoint restrained dominating set of πΊ is the set πΆ = π· βͺ π β π(πΊ). In this paper, we investigate the concept and give some important results on disjoint restrained domination arising from the join and corona of two graphs.
