Degree-diameter problem $N(4,6)$
The largest possible number of vertices in a graph of maximum degree $4$ and diameter at most $6$.
Lower bound:
$760$
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:
$513$
Checked construction
degree-diameter-4-6-lower-513, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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1994-11-03
Lower bound: $740$
Comellas, F., & Gómez, J. (1994). New large graphs with given degree and diameter. arXiv preprint math/9411218.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $760$
Nishant Bhakar in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]