Connectivity of the Mycielskian of a graph

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 μ(G)μ(G), which is called the Mycielskian of G  . This paper investigates the vertex-connectivity κ(μ(G))κ(μ(G)) and edge-connectivity κ′(μ(G))κ′(μ(G)) of μ(G)μ(G) . We show that κ(μ(G))=min{δ(μ(G)),2κ(G)+1}κ(μ(G))=min{δ(μ(G)),2κ(G)+1} and κ′(μ(G))=δ(μ(G))κ′(μ(G))=δ(μ(G)).