Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

Masoumeh Akbarizadeh (), Mehdi Alaeiyan () and Raffaele Scapellato ()
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Masoumeh Akbarizadeh: Iran University of Science and Technology, Narmak
Mehdi Alaeiyan: Iran University of Science and Technology, Narmak
Raffaele Scapellato: Politecnico di Milano

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1919-1930

Abstract: 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}.

Keywords: Non-solvable group; arc transitive; pentavalent digraph; coset digraph; 05C25; 20B25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0504-7

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