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Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

Author

Listed:
  • Masoumeh Akbarizadeh

    (Iran University of Science and Technology, Narmak)

  • Mehdi Alaeiyan

    (Iran University of Science and Technology, Narmak)

  • Raffaele Scapellato

    (Politecnico di Milano)

Abstract

A digraph $$\overrightarrow {\rm{\Gamma}} $$ Γ → is said to be 1-transitive if its automorphism group acts transitively on the 1-arcs but not on the 2-arcs of $$\overrightarrow {\rm{\Gamma}} $$ Γ → . We give a tentatively complete classification of pentavalent strongly connected 1-transitive digraphs of order 2apbq, where p and q are two distinct odd primes, a ∈ {3,…, 8},b ∈ {1, …, 4}, whose automorphism groups are non-solvable. It is shown that such digraphs exist if and only if q = 3 or 13 and p ∈ {7, 11, 17, 19, 31, 41}.

Suggested Citation

  • Masoumeh Akbarizadeh & Mehdi Alaeiyan & Raffaele Scapellato, 2020. "Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1919-1930, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0504-7
    DOI: 10.1007/s13226-020-0504-7
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    References listed on IDEAS

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    1. Mehdi Alaeiyan & Masoumeh Akbarizadeh, 2019. "Classification of the pentavalent symmetric graphs of order 18p," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(2), pages 485-497, June.
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