Analysis of Properties of Fuzzy Graphs

The purpose of this thesis is to investigate the properties of the combination of graph theory and fuzzy set theory called fuzzy graph. The crisp and fuzzy graphs are compared. The operations on fuzzy relations are performed. The max-min and max-product compositions of fuzzy relations are illustrated. α-cut of fuzzy relations is presented. The different types of fuzzy relations are investigated. The Cartesian product, union and join operations on fuzzy graph are studied. Such properties of fuzzy graph as fuzzy and partial fuzzy subgraphs, complement of fuzzy graph, degrees and total degrees of vertices of fuzzy graph, regular and totally regular fuzzy graphs, complete fuzzy graph, and fuzzy tree are analyzed.