Novel concepts of domination in vague graphs with application in medicine. (English) Zbl 1512.05327
Summary: VG can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. The previous definitions’ restrictions in FGs have made us present new definitions in VGs. A wide range of applications have been attributed to the domination in graph theory for several fields such as facility location problem, school bus routing, modeling biological networks, and coding theory. Therefore, in this research, we study several concepts of domination, such as restrained dominating set (RDS), perfect dominating set (PDS), global restrained dominating set (GRDS), total \(k\)-dominating set, and equitable dominating set (EDS) in VGs and also introduce their properties by some examples. Finally, we try to represent the application and importance of domination in the field of medical science and discuss the topic in today’s world, namely, the corona vaccine.
MSC:
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05C72 | Fractional graph theory, fuzzy graph theory |
| 92C50 | Medical applications (general) |
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