On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order  

作　　者：Yan-quanFeng JinHoKwak Ming-yaoXu 

机构地区：[1]DepartmentofMathematics,NorthernJiaotongUniversity,Beijing100044,China [2]CombinatorialandComputationalMathematicsCenter,PohangUniversityofScienceandTechnology,Pohang,790-784,Korea [3]LaboratoryforMathematicsandAppliedMathematics,InstituteofMathematics,PekingUniversity,Beijing100871,China

出　　处：《Acta Mathematicae Applicatae Sinica》2003年第1期83-86,共4页应用数学学报（英文版）

基　　金：Supported by the NNSFC (No.19831050),RFDP (No.97000141), SRF for ROCS,EYTP in China and Com~2MaC-KOSEF in Korea.

摘　　要：Abstract Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^k (kS1), 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 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^k (kS1) is at most 1-arc-transitive for p p 5 and 2-arc-transitive for p = 5.Abstract Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^k (kS1), 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 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^k (kS1) is at most 1-arc-transitive for p p 5 and 2-arc-transitive for p = 5.

关 键 词：Keywords Cayley graphs s -arc-transitive VERTEX-TRANSITIVE 

分 类 号：O157.5[理学—数学] O152[理学—基础数学]