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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Northern Jiaotong University, Beijing, 100044, China

    Yan-quan Feng

  2. Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, Pohang, 790-784, Korea

    Jin Ho Kwak

  3. Laboratory for Mathematics and Applied Mathematics, Institute of Mathematics, Peking University, Beijing, 100871, China

    Ming-yao Xu

Authors
  1. Yan-quan Feng
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  2. Jin Ho Kwak
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  3. Ming-yao Xu
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Corresponding author

Correspondence to Yan-quan Feng.

Additional information

Supported by the NNSFC (No. 19831050), RFDP (No. 97000141), SRF for ROCS, EYTP in China and Com2MaC-KOSEF in Korea.

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Feng, Yq., Kwak, J. & Xu, My. On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order. Acta Mathematicae Applicatae Sinica, English Series 19, 83–86 (2003). https://doi.org/10.1007/s10255-003-0083-5

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  • DOI: https://doi.org/10.1007/s10255-003-0083-5

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