THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn

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 | (Ay ∈ 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.