Abstract
In this work is proven the existence of non-Cayley vertex-transitive tournaments of order p k , for each prime p ⩾ 3 and k ⩾ 4 , and an explicit construction is given. These tournaments are special cases of ( p k - 1 , p ) -metacirculant digraphs, and have the same automorphism group as the first non-Cayley vertex-transitive digraphs of order p k , given by Marušič in 1985. Moreover, from these tournaments, new non-Cayley vertex-transitive tournaments that realise many more degrees are constructed.
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