Clawfreeness of the powers of a graph

Let n∈Nn∈N. We describe a list GnGn of graphs such that if the nnth power GnGn of a graph GG contains a claw then some graph in GnGn appears as an induced subgraph of GG. We show that our set GnGn is the smallest set of graphs with this property. If TT is a tree, this gives a precise characterization of the claw-free powers of TT.