The distance-regular graphs with intersection number \(a_1\neq 0\) and with an eigenvalue \(-1-(b_1/2)\) (Q1280306)

The author refines \textit{P. Terwilliger}'s earlier result in [Discrete Math. 61, 311-315 (1986; Zbl 0606.05045)] that says if the intersection number \(b_1 \not = 0\) for a distance-regular graph, then all eigenvalues are equal to or greater than \(-(b_1/2)-1\). The distance-regular graphs of non-zero intersection number and with eigenvalue \(-(b_1/2)-1\) are listed.