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The aim of this paper is to introduce the extension of intuitionistic fuzzy threshold graph to Neutrosophic field of approach. A new structure called Neutrosophic fuzzy threshold graph (NFTG) have been portrayed and the Neutrosophic fuzzy alternating 4-cycle have been explained using suitable examples. Two parameters namely, Neutrosophic fuzzy threshold dimension and Neutrosophic fuzzy threshold partition number have been illustrated with examples. Theorems based on proposed concepts were proved and one application has been discussed to insist the utility of Neutrosophic fuzzy threshold graph in resource management technique.