Hubbi Muhammad, Rambu Maya Imung Maharani, Sri Nurhayati, Mira Wadu, Yeni Susanti
{"title":"THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn","authors":"Hubbi Muhammad, Rambu Maya Imung Maharani, Sri Nurhayati, Mira Wadu, Yeni Susanti","doi":"10.22342/jims.30.1.1401.110-120","DOIUrl":null,"url":null,"abstract":"We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G \\ B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/jims.30.1.1401.110-120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G \ B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn