Infinite families of non-Cayley vertex-transitive tournaments

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