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A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers (1706.03132v1)
Published 9 Jun 2017 in math.CO
Abstract: 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.
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