THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn

Hubbi Muhammad (Universitas Pamulang)
Rambu Maya Imung Maharani (Universitas Gadjah Mada)
Sri Nurhayati (Universitas Gadjah Mada)
Mira Wadu (Universitas Gadjah Mada)
Yeni Susanti (Universitas Gadjah Mada)

Journal of the Indonesian Mathematical Society
VOLUME 30 NUMBER 1 (MARCH 2024)

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