Radio Number of Hamming Graphs of Diameter 3

For $G$ a simple, connected graph, vertex labeling $f:V(G)\to \Z_+$ is called \emph{radio of $G$} if it satisfies $|f(u)-f(v)|\geq\diam(G)+1-d(u,v)$ for all distinct vertices $u,v\in V(G)$. The number the minimal span over radio labelings $G$. If bijective onto $\{1,2,\dots,|V(G)|\}$ exists, graceful} graph. We determine diameter 3 Hamming graphs and show that an infinite subset them graceful.