Spectral characterization of the Hamming graphs (Q952057)

It is shown that the Hamming graph \(H(3,q)\) with diameter three is uniquely determined by its spectrum for \(q\geq 36\). It is also demonstrated that for given integer \(D\geq 2\), any graph cospectral with the Hamming graph \(H(D,q)\) is locally the disjoint union of \(D\) copies of the complete graph of size \(q-1\), for \(q\) large enough.