Kurniawan Sugiarto, Mamika Ujianita Romdhini, Ni Wayan Switrayni
Zero-divisor graphs of a commutative ring with identity has 3 specific simple forms, namely star zero-divisor graph, complete zero-divisor graph and complete bipartite zero-divisor graph. Graph automorphism is one of the interesting concepts in graph theory . Automorphism of graph G is an isomorphism from graph G to itself. In other words, an automorphism of a graph G is a permutation φ of the set points V(G) which has the property that (x,y) in E(G) if and only if (φ(x),φ(y)) in E(G), i.e. φ preserves adjacency.This study aims to analyze the form of zero-divisor graph automorphisms of a commutative ring with identity formed. The method used in this study was taking sampel of each zero-divisor graph to represent each graph. Thus, pattern and shape of automorphism of each graph can be determined. Based on the results of this study, a star zero-divisor graph with pattern K_1,(p-1), where p is prime, has (p-1)! automorphisms, a complete zero-divisor graph with pattern K_(p-1), where p is prime, has (p-1)! automorphisms, and a complete bipartite zero-divisor graph with pattern K_(p-1),(q-1), where p is prime, has (p-1)!(q-1)! automorphisms, when p not equals to q and 2((p-1)!(q-1)!) automorphisms when p=q.
{"title":"Analisis Automorfisma Graf Pembagi-nol dari Ring Komutatif dengan Elemen Satuan","authors":"Kurniawan Sugiarto, Mamika Ujianita Romdhini, Ni Wayan Switrayni","doi":"10.29303/EMJ.V1I1.11","DOIUrl":"https://doi.org/10.29303/EMJ.V1I1.11","url":null,"abstract":"Zero-divisor graphs of a commutative ring with identity has 3 specific simple forms, namely star zero-divisor graph, complete zero-divisor graph and complete bipartite zero-divisor graph. Graph automorphism is one of the interesting concepts in graph theory . Automorphism of graph G is an isomorphism from graph G to itself. In other words, an automorphism of a graph G is a permutation φ of the set points V(G) which has the property that (x,y) in E(G) if and only if (φ(x),φ(y)) in E(G), i.e. φ preserves adjacency.This study aims to analyze the form of zero-divisor graph automorphisms of a commutative ring with identity formed. The method used in this study was taking sampel of each zero-divisor graph to represent each graph. Thus, pattern and shape of automorphism of each graph can be determined. Based on the results of this study, a star zero-divisor graph with pattern K_1,(p-1), where p is prime, has (p-1)! automorphisms, a complete zero-divisor graph with pattern K_(p-1), where p is prime, has (p-1)! automorphisms, and a complete bipartite zero-divisor graph with pattern K_(p-1),(q-1), where p is prime, has (p-1)!(q-1)! automorphisms, when p not equals to q and 2((p-1)!(q-1)!) automorphisms when p=q.","PeriodicalId":281429,"journal":{"name":"EIGEN MATHEMATICS JOURNAL","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125350124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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