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In this paper, we introduce and study the graph of the groups of mappings ona set X with respect to function compositions that cannot be subsets of thesymmetric groups S3 and S4. Furthermore, we investigate some of thejustifications on these groups that have studied in graph theory, and we gotgood results. Moreover, we consider the graph of these groups by fixed pointsand study some properties of it.

Graph of NG groups not subset of S3 and S4