Spectral Characterization of the Hamming Graphs

Abstract

We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q is greater than or equal to 36. Moreover, we show that for given integer D greater than or equal to 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.