Some Types of Domination in Vague Graphs with Application in Medicine

Fuzzy graphs and algorithms based on them can be very useful for the solution of many problems of practical interest. Since the uncertain and imprecise information is an essential characteristic feature virtually all real life problems, mostly uncertain, the modeling of such such problems using fuzzy graphs is difficult, even for an expert. A vague graph, an extension of the basic concept of a fuzzy graph, can be employed to deal with deeper aspects of uncertainty and imprecision for which the use of fuzzy graphs would not fully succeed. Domination is one of the most important issue in graph theory and has found many applica-tions for the formulation and solution of many problems in various areas of science and technology exemplified by computer networks, artificial intelligence, combinatorial analyses, coding theory, etc. The concept of domination has been extended to fuzzy graphs, and vague graphs, to just name a few. We discuss here different concepts and properties related to domination in vague graphs such as an edge dominating set, an edge independent set, regular dominating set, regular independent set, and global dominating set, with some examples. Finally, we show an appli-cation of domination in vague graphs in the field of medicine that is related to the Influenza vaccine.