Non-Braid Graphs of Ring Zn

Authors

  • Era Setya Cahyati Universitas Gadjah Mada
  • Rizka 'Abid Fadhiilah Universitas Gadjah Mada
  • Ananditya Dwi Candra Bp Universitas Gadjah Mada
  • Indah Emilia Wijayanti Universitas Gadjah Mada

DOI:

https://doi.org/10.31764/jtam.v6i1.5559

Keywords:

Non-braid graphs, Ring Zn, Complete graphs, Connected graphs.

Abstract

The research in graph theory has been widened by combining it with ring. In this paper, we introduce the definition of a non-braid graph of a ring.  The non-braid graph of a ring R, denoted by YR, is a simple graph with a vertex set R\B(R), where B(R) is the set of x in R such that  xyx=yxy for all y in R.  Two distinct vertices x and y are adjacent if and only if xyx not equal to yxy.  The method that we use to observe the non-braid graphs of Zn is by seeing the adjacency of the vertices and its braider.  The main objective of this paper is to prove the completeness and connectedness of the non-braid graph of ring Zn. We prove that if n is a prime number, the non-braid graph of Zn is a complete graph. For all n greater than equal to 3,  the non-braid graph of Zn is a connected graph.

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Published

2022-01-22

Issue

Vol. 6 No. 1 (2022): January

Section

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