| 广义四元数群的4-度Cayley图 |
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| 引用本文： | 仝允战,袁德有. 广义四元数群的4-度Cayley图[J]. 数学的实践与认识, 2006, 36(12): 269-273 |
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| 作者姓名： | 仝允战 袁德有 |
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| 作者单位： | 1. 郑州轻工业学院信息与计算科学系,郑州,450002
2. 南阳理工学院应用数学系,南阳,473000 |
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| 摘 要： | 一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题.
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| 关 键 词： | 广义四元数群 Cayley图 全自同构群 正规性 正则性 字典式积 |
| 修稿时间： | 2005-06-19 |
4-valent Cayley Graphs of Generalized Quaternion Groups |
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| TONG Yun-zhan,YUAN De-you. 4-valent Cayley Graphs of Generalized Quaternion Groups[J]. Mathematics in Practice and Theory, 2006, 36(12): 269-273 |
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| Authors: | TONG Yun-zhan YUAN De-you |
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| Abstract: | A group G is said to be a generalized quaternion groups,if Q_(4p)=〈a,b|a~(2n)=1,b~2=a~n,a~b=a~(-1)〉,p3.According to the generalized quaternion group Q_(4p) has only two classes subsets whose numbers of generators are 2,moreover,they are transitive under Aut(Q_(4p)).Combine the concrete graphs,the method that makes use of to check the circle proved the normality and regularity of 4-Cayley graphs of Q_(4p) about these two subsets of generators.Resolved complete classification problem of 4-valent Cayley graphs. |
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| Keywords: | generalized quaternion group Cayley-graph groups of all automorphism normality regularity dictionary products |
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