Abstract
A digraph \(\overrightarrow {\rm{\Gamma}} \) is said to be 1-transitive if its automorphism group acts transitively on the 1-arcs but not on the 2-arcs of \(\overrightarrow {\rm{\Gamma}} \). 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}.
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Akbarizadeh, M., Alaeiyan, M. & Scapellato, R. Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups. Indian J Pure Appl Math 51, 1919–1930 (2020). https://doi.org/10.1007/s13226-020-0504-7
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DOI: https://doi.org/10.1007/s13226-020-0504-7