Current perspectives of fuzzy graph theory and its applications

This thesis is a review study on fuzzy graph theory and some of its applications. The purpose of the thesis is to address and review some of the previous studies of the fuzzy graph theory and to mention how it has been developed and utilized in solving various real-life problems and to explain the basic concepts that should be known about this fascinating field of mathematics. To summarize in outline: In the introduction chapter, the thesis problem and the historical sequence of the thesis topic were briefly presented. In the preliminary chapter, some basic definitions, theorems, and examples about fuzzy sets, graph theory, and fuzzy graph theory, which are prerequisites for the reader to understand the content of the thesis, were given. In the third chapter, some applications of fuzzy graphs in communications and networking, in competition in the manufacturing industries, as well as various applications of fuzzy graph coloring were introduced with some examples. In the fourth chapter of the thesis, before the conclusions and recommendation chapter, a brief literature review on the subject of the thesis was presented by scanning some of the MSc and PhD theses about fuzzy graph theory. It is self-evident that by making use of these theses and their reference lists, many research articles, theses, many other sources, and open problems, etc., about fuzzy graph theory and its real-life applications can be accessed.