On the Koolen-Park inequality and Terwilliger graphs (Q1960279)

Summary: \textit{J. H. Koolen} and \textit{J. Park} [Eur. J. Comb. 31, No. 8, 2064--2073 (2010; Zbl 1221.05117)] proved a lower bound for the intersection number \(c_2\) of a distance-regular graph \(\Gamma\). Moreover, they showed that a graph \(\Gamma \), for which equality is attained in this bound, is a Terwilliger graph. We prove that \(\Gamma\) is the icosahedron, the Doro graph or the Conway-Smith graph if equality is attained and \(c_2\geq 2\).