On the eigenvectors of the quotient matrix of a perfect coloring of a Q-polynomial graph.

In the decomposition of the element-wise (Hadamard) product of two eigenvectors of the quotient matrix of a perfect coloring into a linear combination of basis eigenvectors, the indices of non-zero coefficients must satisfy the triangle inequality in the Q-polynomial indexing of the eigenvalues of the ambient graph. This new observation kills many putative intersection arrays in the small parameter tables of completely regular codes in Hamming graphs.