A remark on bipartite distance-regular graphs of even valency
Let \(\Gamma\) be a distance-regular graph with the intersection numbers \(p^s_{i,j}\), that is the number of vertices \(x\) with \(\delta(u, x)= i\) and \(\delta(v, x)= j\) for \(u, v\in \Gamma\) at distance \(s= \delta(u, v)\). The author establishes the following theorem: Given a bipartite distance-regular graph \(\Gamma\) with even valency \(b_0\) and \(t> 1\) the length of any series of \((1, 0, 1)\)'s in the intersection array modulo 2, then \(t+ 1\mid r_1+ 1\), with \(r_1\) the length of the first series and \(b_0= p^0_{1,1}\).
scientific article; zbMATH DE number 784143