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21.90 (2026)

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Let $\Gamma$ be a graph of diameter $d$. For $i \in \{1, 2, \dots, d\}$, let $\Gamma_i$ be the graph on the same vertex set as $\Gamma$ with vertices $u, w$ adjacent in $\Gamma_i$ if and only if $d_\Gamma(u, w) = i$. Does there exist a $Q$-polynomial distance-regular graph $\Gamma$ of diameter 3 such that $\Gamma_2$ and $\Gamma_3$ are strongly regular?

Contributor: A. A. Makhnëv

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