| 定义在有限群上的一类新的共轭类图 |
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| 引用本文： | 韦华全,田梦飞,杨立英,张英杰,马儇龙.定义在有限群上的一类新的共轭类图[J].广西师院学报,2013(4):13-17. |
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| 作者姓名： | 韦华全 田梦飞 杨立英 张英杰 马儇龙 |
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| 作者单位： | [1]广西大学数学与信息科学学院,广西南宁530004 [2]广西师范学院数学科学学院,广西南宁530023 |
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| 基金项目： | 国家自然科学基金（11361006;11161006） |
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| 摘 要： | 设G是一个有限群，在G上定义一类新的共轭类图ΓG ：以G的所有共轭类构成的集合为顶点集，两个不同的共轭类之间用一条边相连当且仅当这两个共轭类的长度互素．通过定义的共轭类图得到了一些图性质且通过图性质刻画了一些群的结构，如ΓG 碖 K 3当且仅当G 碖 Z3或S 3．特别地，获得了二面体群共轭类图的一些性质．最后，应用共轭类图的性质得到了一些群的性质．
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| 关 键 词： | 有限群 共轭类 共轭类图 连通图 完全图 |
A New Graph of Conjugacy Classes Associated with Finite Groups |
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| WEI Huaquan,TIAN Mengfei,YANG Liying,ZHANG Yingjie,MA Xuanlong.A New Graph of Conjugacy Classes Associated with Finite Groups[J].Journal of Guangxi Teachers College(Natural Science Edition),2013(4):13-17. |
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| Authors: | WEI Huaquan TIAN Mengfei YANG Liying ZHANG Yingjie MA Xuanlong |
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| Institution: | 1. School of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China; 2. School of Mathematical Sciences, Guangxi Teachers Education University,Nanning 530023, China ) |
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| Abstract: | A new graph ΓG of conjugacy classes of a finite group G is defined ：its verticesare the conjugacy classes of G and two distinct vertices join by an edge if their sizes are coprime .By the defini-tion of ΓG ,we obtain some graph theoretical properties of ΓG and characterize some structures of fi-nite groups by their conjugate graphs .For example ,ΓG ≌ K3 if and only if G≌ Z3 or S3 .In particu-lar ,we prove some properties of the conjugate graphs of dihedral groups .Finally ,we obtain some properties of finite groups by applying properties of the conjugate graphs of finite groups . |
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| Keywords: | finite group conjugacy class conjugate graph connected graph complete graph |
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