In 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 (p k-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. © 2004 Elsevier B.V. All rights reserved.
Mansilla, S. P. (2004). Infinite families of non-Cayley vertex-transitive tournaments. Discrete Mathematics, 288(1–3), 99–111. https://doi.org/10.1016/j.disc.2004.08.002