On Some Regular Properties of Fuzzy Graph

Abstract

Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis, we study the definition of fuzzy graph, complete fuzzy graph, strong fuzzy graph, regular fuzzy graph, totally regular fuzzy graph with illustrative example and properties of regular and totally regular fuzzy graph. We discuss the concept of uniform vertex and uniform edge fuzzy graph with examples also we check the results related to uniform vertex and uniform edge fuzzy graph. We see that the concept of uniform vertex and uniform edge fuzzy graph is useful in the study of regular and totally regular fuzzy graph. We also see the definition of complement of fuzzy graph and properties of self-complement fuzzy graph and we study some other operations on fuzzy graph such that union, join, composition, direct product, semi strong product and strong product. We read the notion of balanced fuzzy graph. At last we see the fuzzy soft graph, complete fuzzy soft graph, regular fuzzy soft graph, totally regular fuzzy soft graph with examples and some of their important properties. My thesis comprising of seven chapters. In the first chapter we will define of fuzzy graph regular fuzzy graph and totally regular fuzzy graph. In the 2th chapter, we will define uniform vertex fuzzy graph and uniform edge fuzzy graph. In the 3th chapter, we will discuss complement of fuzzy graph. We will check union and join of two fuzzy graphs. In the 4th chapter, we will discuss three more operations on fuzzy graph. In the 5th chapter, we will see the concept of the fuzzy soft graph and various types of fuzzy soft graph with examples. In the 6th chapter, we will present the conclusion of our thesis. In the 7th chapter, we will present the references of our thesis.