Degree-diameter problem $N(12,3)$
The largest possible number of vertices in a graph of maximum degree $12$ and diameter at most $3$.
Lower bound:
$810$
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.
-
Lower bound:
$558$
Checked construction
degree-diameter-12-3-lower-558, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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2008-06-03
Lower bound: $786$
Gómez, J. (2009), Some new large (Δ, 3)-graphs. Networks, 53: 1-5.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $810$
Dharunish Yugeswardeenoo in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]