| On the Stabilizer of the Automorphism Group of a 4—valent Vertex—transitive Graph with Odd—prime—power Order |
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| 作者姓名： | Yan-quanFeng JinHoKwak Ming-yaoXu |
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| 作者单位： | [1]DepartmentofMathematics,NorthernJiaotongUniversity,Beijing100044,China [2]CombinatorialandComputationalMathematicsCenter,PohangUniversityofScienceandTechnology,Pohang,790-784,Korea [3]LaboratoryforMathematicsandAppliedMathematics,InstituteofMathematics,PekingUniversity,Beijing100871,China |
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| 基金项目： | Supported by the NNSFC (No.19831050),RFDP (No.97000141), SRF for ROCS,EYTP in China and Com~2MaC-KOSEF in Korea. |
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| 摘 要： | Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^κ（κ≥1） and let A be the full automorphism group of X.In this paper,we prove that the stabilizer Av of a vertex v in A is a 2-group if p≠5,or a {2,3}-group if p=5.Furthermore,if p=5|Av| is not divisible by 3^2.As a result ,we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p^κ(κ≥1） is at most 1-arc-transitive for p≠5 and 2-arc-transitive for p=5.
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| 关 键 词： | 迷向群 自同构群 顶点可迁图 奇素幂阶 Cayley图 |
On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order |
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| Yan-quanFeng JinHoKwak Ming-yaoXu.On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order[J].Acta Mathematicae Applicatae Sinica,2003,19(1):83-86. |
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| Authors: | Email author" target="_blank">Yan-quan?FengEmail author Jin Ho?Kwak Ming-yao?Xu |
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| Institution: | (1) Department of Mathematics, Northern Jiaotong University, Beijing 100044, China (E-mail: yqfeng@center.njtu.edu.cn), CN;(2) Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, Pohang, 790-784, Korea (E-mail: jinkwak@postech.ac.kr), KR;(3) Laboratory for Mathematics and Applied Mathematics, Institute of Mathematics, Peking University, Beijing 100871, China (E-mail: xumy@math.pku.edu.cn), CN |
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| Abstract: | |
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| Keywords: | Cayley graphs s-arc-transitive vertex-transitive |
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