Abstract
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.
Highlights
Graph theory began its adventure from the well-known “Konigsberg bridge problem.” is problem is frequently believed to have been the beginning of graph theory
In this research, we introduce different concepts of domination, such as restrained dominating set (RDS), perfect dominating set (PDS), global restrained dominating set (GRDS), equitable dominating set (EDS), and total k-dominating set in VGS
It is clear that S1 has the smallest size among other RDSs, so we conclude that it can be the best choice because, first, China has the most effective vaccine in terms of susceptibility to the virus, and, second, there is a relatively good friendship between Iran and China. erefore, governments must provide the necessary facilities for the delivery of efficient and useful vaccines to deprived countries in order to prevent the transmission of this deadly virus to the rest of the people as soon as possible
Summary
Graph theory began its adventure from the well-known “Konigsberg bridge problem.” is problem is frequently believed to have been the beginning of graph theory. The dominance of FGs has been stated by some researchers, due to the fact that VGs are wider and are more widely used than FGs, it is observed today that they are used in many branches of engineering and medical sciences Likewise, they have been used in many applications for the formulation and solution of many problems in various areas of science and technology exemplified by computer networks, combinatorial analyses, physics, and so forth. Somasundaram [43] introduced the DS and IDS in FGs. Gani et al [44, 45] represented the fuzzy-DS and independent-DS notion utilizing strong arcs. Talebi et al [52,53,54] introduced some results of domination in VGs, as well as new concepts in interval-valued intuitionistic fuzzy competition graph. An application of domination in medical immunization is introduced
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