Erdős-Rényi theory for asymmetric digraphs

Shohei Satake, Masanori Sawa, Masakazu Jimbo
2018 SLUT journal of mathematics  
We introduce the concept of the asymmetry number for finite digraphs, as a natural generalization of that for undirected graphs by Erdős and Rényi in 1963. 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 Aut(RO).
doi:10.55937/sut/1547570388 fatcat:3r2rgpnqsreclck4rb6ym522y4