On Commuting Graph of Group Ring Z_nS_3  

作　　者：GAO YAN-YAN TANG GAO-HUA CHEN JIAN-LONG 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing, 210096 [2]School of Mathematical Sciences, Guangxi Education University, Nanning, 530001

出　　处：《Communications in Mathematical Research》2012年第4期313-323,共11页数学研究通讯（英文版）

基　　金：The NSF(10971024)of China;the Specialized Research Fund(200802860024)for the Doctoral Program of Higher Education;the NSF(BK2010393)of Jiangsu Province

摘　　要：The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.

关 键 词：group ring commuting graph connected component diameter of agraph 

分 类 号：O153.3[理学—数学] O157.5[理学—基础数学]