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No hexavalent half-arc-transitive graphs of order twice a prime square exist

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Abstract

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set and edge set, but not arc set. Let p be a prime. Wang and Feng (Discrete Math. 310 (2010) 1721–1724) proved that there exists no tetravalent half-arc-transitive graphs of order \(2p^2\). In this paper, we extend this result to prove that no hexavalent half-arc-transitive graphs of order \(2p^2\) exist.

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Authors and Affiliations

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

    Mi-Mi Zhang

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  1. Mi-Mi Zhang
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Correspondence to Mi-Mi Zhang.

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Communicating Editor: B Sury

Appendix

Appendix

In this section, we give the Magma codes to check whether there hexavalent half-arc-transitive 2-type bi-Cayley graphs over P exist or not, where \(|P|=p^{2}\) and \(p=5\) or 7.

Case 1. \(P\cong {\mathbb {Z}}_{p^{2}}\).

figure a

Case 2. \(P\cong {\mathbb {Z}}_{p}\times {\mathbb {Z}}_{p}\).

figure b

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Zhang, MM. No hexavalent half-arc-transitive graphs of order twice a prime square exist. Proc Math Sci 128, 3 (2018). https://doi.org/10.1007/s12044-018-0385-4

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  • DOI: https://doi.org/10.1007/s12044-018-0385-4

Keywords

2010 Mathematics Subject Classification

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