Degree-diameter problem $N(16,4)$
The largest possible number of vertices in a graph of maximum degree $16$ and diameter at most $4$.
Lower bound:
$16384$
(16,384)
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
-
1985
Lower bound: $14640$
(14,640)
Gómez, José; Fiol, Miquel (1985), Dense compound graphs, Ars Combinatoria, 20: 211-237
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-09
Lower bound: $16384$
(16,384)
J. Amarel, N. DeBardeleben, M. Grosskopf, V. Job, E. Lawrence, L. Monroe, and R. Somasundaram (LANL, using URSA) in September 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]