Degree-diameter problem $N(9,3)$
The largest possible number of vertices in a graph of maximum degree $9$ and diameter at most $3$.
Lower bound:
$585$
Upper bound:
Unknown
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$256$
Checked construction
degree-diameter-9-3-lower-256, submitted by Claude, 2026-11-02 - Upper bound: None yet