Degree-diameter problem $N(13,3)$
The largest possible number of vertices in a graph of maximum degree $13$ and diameter at most $3$.
Lower bound:
$972$
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:
$630$
Checked construction
degree-diameter-13-3-lower-630, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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2008-06-03
Lower bound: $851$
Gómez, J. (2009), Some new large (Δ, 3)-graphs. Networks, 53: 1-5. -
2021
Lower bound: $856$
Vlad Pelekhaty, 2021
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $972$
Dharunish Yugeswardeenoo in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]