Abstract
The eigenvalues of the Hamming graph H(n,q) are known to be λi(n,q)=(q−1)n−qi, 0≤i≤n. The characterization of equitable 2-partitions of the Hamming graphs H(n,q) with eigenvalue λ1(n,q) was obtained by Meyerowitz (2003). We study the equitable 2-partitions of H(n,q) with eigenvalue λ2(n,q). We show that these partitions are reduced to equitable 2-partitions of H(3,q) with eigenvalue λ2(3,q) with the exception of two constructions.
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