On the Terwilliger algebra of bipartite distance-regular graphs with Delta(2)=0 and c(2)=2

摘要

Let Gamma denote a bipartite distance-regular graph with diameter D >= 4 and valency k >= 3. Let X denote the vertex set of Gamma, and let A denote the adjacency matrix of Gamma. For x is an element of X and for 0 <= i <= D, let Gamma(i)(x) denote the set of vertices in X that are distance i from vertex x. Define a parameter Delta(2) in terms of the intersection numbers by Delta(2) = (k - 2)(c(3) - 1) - (c(2) - 1)p(22)(2). It is known that Delta(2) = 0 implies that D <= 5 or c(2) is an element of {1, 2}.