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Era Setya Cahyati
Dept. of Mathematics, Gadjah Mada University, Indonesia
Decision Sciences, Operations Research & Management

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GENERALIZED NON-BRAID GRAPHS OF RINGS Era Setya Cahyati; Rambu Maya Imung Maharani; Sri Nurhayati; Yeni Susanti
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 2 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i2.14152

Abstract

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 $B^k(R):=\{x \in R~|~\forall y \in R,~ (xyx)^k = (yxy)^k\}$. The generalized non-braid graph of $R$, denoted by $G_k(\Upsilon_R)$, is a simple undirected graph with vertex set $R\backslash B^k(R)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $(xyx)^k \neq (yxy)^k$. In particular, we investigate some properties of generalized non-braid graph $G_k(\Upsilon_{\mathbb{Z}_n})$ of the ring $\mathbb{Z}_n$.
Co-Authors Rambu Maya Imung Maharani Sri Nurhayati Yeni Susanti