The last subconstituent of a bipartite Q-polynomial distance-regular graph

John S. Caughman
2003 European journal of combinatorics (Print)  
Let Γ denote a bipartite distance-regular graph with diameter D ≥ 3. Fix any vertex x and let denote the graph with vertex set Γ D , and edge set consisting of all pairs of vertices in Γ D which are at distance 2 in Γ . In this paper, we assume Γ is Q-polynomial and show Γ 2 D is distance-regular and Q-polynomial. We compute the intersection numbers of Γ 2 D from the intersection numbers of Γ . To obtain our results, we use a characterization of the Q-polynomial property due to Terwilliger.
doi:10.1016/s0195-6698(03)00059-3 fatcat:kxrdgvurivd3lccs227yzw7iry