GENERALIZED NON-BRAID GRAPHS OF RINGS - Cahyati, Era Setya; Maharani, Rambu Maya Imung; Nurhayati, Sri; Susanti, Yeni (Diponegoro University, 2022)
In this paper, we introduce the definition of generalized non-braid graph of a given ring. Let R be a ring and let k be a natural number. By generalized braider of R we mean the set B^k(R):={x R | y R, (xyx)^k = (yxy)^k}. The generalized non-braid graph of R, denoted by G_k(Υ_R), is a simple undirected graph with vertex set RB^k(R) and two distinct vertices x and y are adjacent if and only if (xyx)^k ≠ (yxy)^k. In particular, we investigate some properties of generalized non-braid graph G_k(Υ_Z_n) of the ring Z_n.