  We extend Hoffman's coclique bound for regular digraphs with the property
that its adjacency matrix is normal, and discuss cocliques attaining the
inequality. As a consequence, we characterize skew-Bush-type Hadamard matrices
in terms of digraphs. We present some normal digraphs whose vertex set is
decomposed into disjoint cocliques attaining the bound. The digraphs provided
here are relation graphs of some nonsymmetric association schemes.
