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Graph plays the role of partial ordering in fuzzy metric spaces. Also, the language of graph in a fuzzy metric space presents a fruitful application of mathematics in computer science and engineering. In this paper, we direct the concept of fuzzy metric space towards the graph theory using altering distance function. Here, to find fixed point, we define a new contraction J-ψ-fuzzy contraction in fuzzy metric space (K, F, *) endowed with a graph.