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We introduce the non-braid graph of a group G, denoted by ζ (G), as a graph with vertex set G\B (G), where B (G) is the braider of G, defined as the set {x∈ G|(∀ y∈ G) xyx= yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸= yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn