Subdivided graphs as isometric subgraphs of Hamming graphs

Isometric subgraphs of Hamming graphs (resp. hypercubes) are called partial Hamming graphs (resp. partial cubes  ). In this paper we look for structural characterizations of subdivided cliques that are partial Hamming graphs. It is proven that given GG a subdivision of a clique KnKn (n≥1n≥1), GG is isometrically embeddable in a Hamming graph if and only if GG is a partial cube or G=KnG=Kn. The characterization for subdivided wheels is also obtained.