Degree-diameter problem $N(8,6)$
The largest possible number of vertices in a graph of maximum degree $8$ and diameter at most $6$.
Lower bound:
$40560$
(40,560)
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: None yet
- Upper bound: None yet
Updates from the literature
-
2008-06-03
Lower bound: $39672$
(39,672)
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: $40560$
(40,560)
Dharunish Yugeswardeenoo in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]