On the Koolen-Park inequality and Terwilliger graphs

Abstract

J.H. Koolen and J. Park proved a lower bound for the intersection number c2 of a distance-regular graph Γ. Moreover, they showed that a graph Γ, for which equality is attained in this bound, is a Terwilliger graph. We prove that γ is the icosahedron, the Doro graph or the Conway-Smith graph if equality is attained and c2 ≥ 2.