A class of self-complementary vertex-transitive digraphs

@article{Chia1986ACO,
title={A class of self-complementary vertex-transitive digraphs},
author={Gek-Ling Chia and Chong-Keang Lim},
journal={Journal of Graph Theory},
year={1986},
volume={10},
pages={241-249}
}

We characterize the class of self-complementary vertex-transitive digraphs on a prime number p of vertices. Using this, we enumerate (i) self-complementary strongly vertex-transitive digraphs on p vertices, (ii) self-complementary vertex-transitive digraphs on p vertices, (iii) selfcomplementary vertex-transitive graphs on p vertices. Finally it is shown that every self-complementary vertex-transitive digraph on p vertices is either a tournament or a graph.