Journal of Fundamental Mathematics and Applications (JFMA)
Vol 5, No 2 (2022)

GENERALIZED NON-BRAID GRAPHS OF RINGS

Era Setya Cahyati (Dept. of Mathematics, Gadjah Mada University, Indonesia)
Rambu Maya Imung Maharani (Departement of Mathematics UGM)
Sri Nurhayati (Department of Mathematics UGM)
Yeni Susanti (Depatment of Mathematics UGM)

Article Info

Publish Date
23 Nov 2022

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 $\mathbb{Z}_n$.

Copyrights © 2022




Citation Download
RIS
EndNote, Reference Manager, ProCite
BibTex
Latex, Jabref
Original Source
Download Original
Google Scholar
Check in Google Scholar
Journal Info
Journal of Fundamental Mathematics and Applications (JFMA)
Website

Abbrev

jfma

Publisher

Universitas Diponegoro

Subject

Decision Sciences, Operations Research & Management

Description

Journal of Fundamental Mathematics and Applications (JFMA) is an Indonesian journal published by the Department of Mathematics, Diponegoro University, Semarang, Indonesia. JFMA has been published regularly in 2 scheduled times (June and November) every year. JFMA is established to highlight the ...