On regular fuzzy resolving set

Abstract

In a fuzzy graph G, if the degree of each vertex is the same, then it is called a regular fuzzy graph. The representation of ? ? H with respect to the subset H of ? are all distinct then H is called the resolving set of the fuzzy graph G(V, ?, µ). In this article, we define a regular fuzzy resolving set, regular fuzzy resolving number and the properties of a regular fuzzy resolving set in a fuzzy graph whose crisp graph is a cycle, even or odd. And also we prove that, if G be a regular fuzzy graph with G* is a cycle, then any minimum fuzzy resolving set of G is a regular fuzzy resolving set of G.