20.53 (2022)
OpenA nonisotropic unitary graph $\Gamma$ is distance-regular with intersection array $\{q(q - 1), (q + 1)(q - 2), q + 1; 1, 1, q(q - 2)\}$ for some prime power $q$. The group $G = \text{Aut}(\Gamma)$ acts transitively on the vertex set and on the edge set of $\Gamma$. It is known that $\Gamma$ is distance-transitive if $q = 3$. Does there exist a distance-regular graph with such an intersection array if $q$ is not a prime power?
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