Degree-diameter problem $N(16,5)$
The largest possible number of vertices in a graph of maximum degree $16$ and diameter at most $5$.
Lower bound:
$153600$
(153,600)
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: $132496$
(132,496)
Delorme, C. (1985). Large bipartite graphs with given degree and diameter. Journal of graph theory, 9(3), 325-334.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10-30
Lower bound: $153600$
(153,600)
Rajiv, R. (2026). New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts. Zenodo.
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]