Two remarks on Huang's characterization of the bilinear forms graphs

In [4] Huang has given a characterization of the bilinear forms graphsHq (n, d) using the weak 4-vertex conditions and a condition on the parametersn, d andq. We show that the weak 4-vertex condition can be replaced by a condition on the eigenvalues of the adjacency matrix of the graph. Furthermore, we show that the conditions on the parameters can be weakened.