Fuzzy Metric Dimension of Fuzzy Hypercube Qn and Fuzzy Boolean Graphs

Abstract

Let G = (V, E, ) be a fuzzy graph. Let M be a subset of V. M is said to be a fuzzy metric basis of G if for every pair of vertices x, y  V ‒ M, there exists a vertex w  M such that d (w, x)  d (w, y). The number of elements in M is said to be fuzzy metric dimension (FMD) of G and is denoted by  (G). The elements in M are called as source vertices. In this paper, we study the fuzzy metric dimension of fuzzy hypercube Qn, fuuzy Boolean Graph BG2 (G) and fuzzy Boolean Graph BG3 (G).