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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika)
Ananditya Dwi Candra Bp
Universitas Gadjah Mada
Mathematics

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Non-Braid Graphs of Ring Zn Era Setya Cahyati; Rizka 'Abid Fadhiilah; Ananditya Dwi Candra Bp; Indah Emilia Wijayanti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 1 (2022): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i1.5559

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.
Co-Authors Era Setya Cahyati Indah Emilia Wijayanti Rizka 'Abid Fadhiilah