Satake, Shohei; Sawa, Masanori; Jimbo, Masakazu Erdős-Rényi theory for asymmetric digraphs. (English) Zbl 1422.05095 SUT J. Math. 54, No. 2, 109-129 (2018). Summary: We introduce the concept of the asymmetry number for finite digraphs, as a natural generalization of that for undirected graphs by P. Erdős and A. Rényi [Acta Math. Acad. Sci. Hung. 14, 295–315 (1963; Zbl 0118.18901)]. We prove an upper bound for the asymmetry number of finite digraphs and give a condition for equality. We show that our bound is asymptotically best for digraphs with sufficiently large order. We also consider the random oriented graph \(RO\), and make some remarks on \(\operatorname{Aut}(RO)\). Cited in 1 Document MSC: 05C80 Random graphs (graph-theoretic aspects) 05C20 Directed graphs (digraphs), tournaments Keywords:asymmetry number; random digraphs; random oriented graph; acyclic random oriented graph Citations:Zbl 0118.18901 PDFBibTeX XMLCite \textit{S. Satake} et al., SUT J. Math. 54, No. 2, 109--129 (2018; Zbl 1422.05095)