Tight distance-regular graphs

Aleksandar Jurisic, Jack Koolen, Paul Terwilliger

We consider a distance-regular graph $\G$ with diameter $d\ge 3$ and eigenvalues $k={\theta }_0>{\theta }_1>...>{\theta }_d$. We show the intersection numbers $a_1,b_1$ satisfy $$ (θ_1 + {k \over a_1+1…