Twice Q-polynomial distance-regular graphs (Q1924162)

Kite numbers are useful parameters of distance-regular graphs. Based on Terwilliger's results, the author obtained a formula, in terms of intersection numbers and dual eigenvalues, for the kite numbers of distance-regular graphs which are Q-polynomial with respect to two distinct eigenvalues. This formula indicates that the kite numbers \(f_{ij}(x,y,z)\) are independent of the vertices \(x\), \(y\), \(z\). As another application, the author showed that the vertex neighborhood graphs of the graphs mentioned above are strongly regular.