Perfect state transfer on distance-regular graphs and association schemes

We consider the representation of a continuous-time quantum walk in a graph X by the matrix exp(-itA(X)). We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to have perfect state transfer. Using these conditions, we provide several new examples of perfect state transfer in simple graphs. (C) 2015 Elsevier Inc. All rights reserved.