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Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphs

Author

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  • Feng, Yan-Quan
  • Hujdurović, Ademir
  • Kovács, István
  • Kutnar, Klavdija
  • Marušič, Dragan

Abstract

A non-trivial automorphism g of a graph Γ is called semiregular if the only power gi fixing a vertex is the identity mapping, and it is called quasi-semiregular if it fixes one vertex and the only power gi fixing another vertex is the identity mapping. In this paper, we prove that K4, the Petersen graph and the Coxeter graph are the only connected cubic arc-transitive graphs admitting a quasi-semiregular automorphism, and K5 is the only connected tetravalent 2-arc-transitive graph admitting a quasi-semiregular automorphism. It will also be shown that every connected tetravalent G-arc-transitive graph, where G is a solvable group containing a quasi-semiregular automorphism, is a normal Cayley graph of an abelian group of odd order.

Suggested Citation

  • Feng, Yan-Quan & Hujdurović, Ademir & Kovács, István & Kutnar, Klavdija & Marušič, Dragan, 2019. "Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphs," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 329-337.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:329-337
    DOI: 10.1016/j.amc.2019.01.048
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    Cited by:

    1. Yin, Fu-Gang & Feng, Yan-Quan, 2021. "Symmetric graphs of valency 4 having a quasi-semiregular automorphism," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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