Degree-diameter problem $N(3,9)$
The largest possible number of vertices in a graph of maximum degree $3$ and diameter at most $9$.
Lower bound:
$600$
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:
$506$
Checked construction
degree-diameter-3-9-lower-506, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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2008-01-28
Lower bound: $600$
Geoffrey Exoo, communicated to F. Comellas on January 28, 2008
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]