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Acta Mathematicae Applicatae Sinica

, Volume 19, Issue 1, pp 83–86 | Cite as

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

  • Yan-quan Feng
  • Jin Ho Kwak
  • Ming-yao Xu
Original Papers

Abstract

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer A v 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 |A v | is not divisible by 32. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.

Keywords

Cayley graphs s-arc-transitive vertex-transitive 

2000 MR Subject Classification

05C25 20B25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsNorthern Jiaotong UniversityBeijingChina
  2. 2.Combinatorial and Computational Mathematics CenterPohang University of Science and TechnologyPohangKorea
  3. 3.Laboratory for Mathematics and Applied Mathematics, Institute of MathematicsPeking UniversityBeijingChina

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