Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

Considering all physical, biological and social systems, fuzzy graph (FG) models serves the elemental processes of all natural and artificial structures. In general, FG-theory has a wide range of applications in various fields. Since the indeterminate information is an essential real-life problem, mostly uncertain, modeling those problems based on FG is highly demanding for an expert. VG can manage the uncertainty, associated with the unpredictable and unspecified data of all real-world problems, in which FGs will conceivably not ensue into generating satisfactory results. Domination is one of the most important issues in graph theory and has found many applications for the formulation and solution of many problems in various areas of science and technology exemplified by computer networks, artificial intelligence, combinatorial analyses, and etc. Therefore, in this paper, we introduce distinctive concepts and properties related to domination in product vague graphs such as edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Today, almost every country in the world is inflicted by a dangerous disease called Covid-19. Unfortunately, many people lost their lives due to contracting this dangerous virus and the lack of necessary medical equipment for treatment. So, we have tried to identify a suitable hospital for a person infected with the corona virus, which has more appropriate medical facilities and equipment, and is in the most favorable condition in terms of distance and amount of traffic, so that save time and money, with help of DS in VG.