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).
Highlights
V V [0,1] where d (vi, vj) = min ( ij(P)) and d (vi, vi) = 0
P Pij For any two fuzzy shortest paths P and Q between vi and vj, we consider the path with lesser number of intermediate vertices
We study the fuzzy metric basis of fuzzy Boolean graph BG2(G) for some standard fuzzy graphs G and fuzzy Boolean graph BG3(G) for some standard fuzzy graphs G
Summary
N(vi, vj) is defined as the number of intermediate vertices between vi and vj in fuzzy shortest path (FSP) and d (vi, vj, t) is denoted as d (vi, vj). 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).
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