| 群环ZnD5的交换图 |
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| 引用本文： | 唐高华,曾庆雨,易忠,崔春强.群环ZnD5的交换图[J].广西师院学报,2013(4):1-7. |
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| 作者姓名： | 唐高华 曾庆雨 易忠 崔春强 |
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| 作者单位： | [1]广西师范学院数学科学科学学院,广西南宁530023 [2]广西民族师范学院数学与计算机科学系,广西崇左532200 |
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| 基金项目： | This research was supported by the National Natural Science Foundation of China （11161006, 11171142）, the Guangxi Natural Science Foundation （2011GXNSFA018139） and Guangxi ＂new century 1000 talents project＂ |
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| 摘 要： | 设 R是一个任意环，Z（R）是R的中心，R的交换图记为Γ（R），它的顶点集为R＼（R），且顶点a和b相连当且仅当它们在R中可交换．该文研究了群环Zn D5的交换图的连通性和直径．主要结果为：若n不等于2或5，那么Γ（Zn D5）是连通的；若Γ（Zn D5）是连通的，则Γ（Zn D5）的直径等于3．
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| 关 键 词： | 群环 交换图 联通分支 直径 |
On Commuting Graph of the Group Ring Z nD5 |
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| TANG Gaohua,ZENG Qingyu,YIZhong,CUI Chunqiang.On Commuting Graph of the Group Ring Z nD5[J].Journal of Guangxi Teachers College(Natural Science Edition),2013(4):1-7. |
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| Authors: | TANG Gaohua ZENG Qingyu YIZhong CUI Chunqiang |
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| Institution: | 1. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023, China 2. Department of Mathematics and Computer Sciences, Guangxi Normal University for Nationalities, Chongzuo 532200, China) |
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| Abstract: | Let R be an arbitrary ring and Z（R） the center of R ,the commuting graph of R ,denotedΓ（R） ,is the graph with the vertex set R／Z（R） ,and two distinct vertices a and b are adjacent if and only if they comute in R .In this paper the connectivity and the diameter of the commuting graph of the group ring ZnD5 are investigated .The main result is that Γ（ZnD5）is connected if n is not equal to 2 or 5 .If Γ（Zn D5 ） is connected ,then diam Γ（Zn D5 ）=3 . |
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| Keywords: | group ring commuting graph connected component diameter of a graph |
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