A study of independency on fuzzy resolving sets of labelling graphs

Abstract

Considering a fuzzy graph G is simple and can be connected and considered as a subset H = { (u(1), s(u(1))), (u(2), s(u(2))), ...(u(k), s(u(k)))}, |H|= 2; then, every two pairs of elements of s - H have a unique depiction with the relation of H, and H can be termed as a fuzzy resolving set (FRS). The minimal H cardinality is regarded as the fuzzy resolving number (FRN), and it is signified by Fr(G). An independence set is discussed on the FRS, fuzzy resolving domination set (FRDS), and Fuzzy modified antimagic resolving set (FMARS). In this paper, we discuss the independency of FRS and FMARS in which an application has also been developed.