A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers

Supalak Sumalroj

Published 2017-06-09Version 1

We consider a primitive distance-regular graph $\Gamma$ with diameter at least $3$. We use the intersection numbers of $\Gamma$ to find a positive semidefinite matrix $G$ with integer entries. We show that $G$ has determinant zero if and only if $\Gamma$ is $Q$-polynomial.