Super connectivity and super arc 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 G into a new graph mu(G), which is called the Mycielskian of G. This paper shows that: for a strongly connected digraph D with vertical bar V(D)vertical bar >= 2, mu(D) is super-kappa if and only if delta(D) < 2 kappa(D); mu(D) is super-lambda if and only if D not congruent to <(K)over right arrow>(2).