Sets of Complex Unit Vectors with Two Angles and Distance-Regular Graphs

We study {0,\alpha}-sets, which are sets of unit vectors of ${\mathbb{C}}^m$ in which any two distinct vectors have angle 0 or \alpha. We investigate some distance-regular graphs that provide new constructions of {0,\alpha}-sets using a method by Godsil and Roy. We prove bounds for the sizes of {0,\alpha}-sets of flat vectors, and characterize all the distance-regular graphs that yield {0,\alpha}-sets meeting the bounds at equality.