Complement of a Fuzzy Graph

Abstract

Fuzzy graph is a graph consists pairs of vertex and edge that have degree of membership containing closed interval of real number [0,1] on each edge and vertex. At first, complement of a fuzzy graph was defined by Mordeson and completed by M.S Sunitha and Vijayakumar. Based on complement of the completed fuzzy graphs , it can be have that double complement of fuzzy graph is that fuzzy graph and will be shown that the automorphism groups of a fuzzy graph and its complement are identical. In this paper will show that the operations of union, join, cartesian product and composition of fuzzy graphs and prove that complement of the union of two fuzzy graphs is the join of their complements and the complement of the join of two fuzzy graphs is the union of their complements. Finally will prove that complement of the composition of two strong fuzzy graphs is the composition of their complements.