Connectivity of the Mycielskian of a digraph

In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph GG into a new graph μ(G)μ(G), which is called the Mycielskian of GG. This work investigates the vertex connectivity and arc connectivity of the Mycielskian of a digraph DD. This generalizes the recent results due to Balakrishnan and Raj [R. Balakrishnan, S.F. Raj, Connectivity of the Mycielskian of a graph, Discrete Math, 308 (2008), 2607–2610].