Distance-regular Subgraphs in a Distance-regular Graph, IV

Let Γ be a distance-regular graph witha1>0, r=max{j|(cj,aj,bj)=(c1,a1,b1)}≥2 andai=a1ci,for 1≤i≤2r.Take anyuandvin Γ at distancer+1. We show that there exists a collinearity graph of a generalized 2(r+1)-gon of order (a1+1, crr+1-1)containinguandvas a subgraph in Γ.