Degree-diameter problem $N(16,7)$
The largest possible number of vertices in a graph of maximum degree $16$ and diameter at most $7$.
Lower bound:
$14995367$
(14,995,367)
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
-
1993-04-28
Lower bound: $14882658$
(14,882,658)
Gómez, J., Fiol, M. A., & Serra, O. (1993). On large (Δ, D)-graphs. Discrete Mathematics, 114(1-3), 219-235.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $14995367$
(14,995,367)
Nishant Bhakar in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]