On radio graceful Hamming graphs of any diameter

We show that Hamming graphs of diameter $D$ are radio graceful provided that each component of the Hamming graph is a complete graph with at least $D$ vertices. This generalizes the results known previously for diameters $D=2$ and $D=3$ and for general $D$ with the assumption that the components of the Hamming graph have the same or pairwise relatively prime numbers of vertices.