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

  • Mi-Mi Zhang


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.


Half-arc-transitive bi-Cayley graph vertex transitive edge transitive 

2010 Mathematics Subject Classification

05C25 20B25 


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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingChina

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