Degree-diameter problem $N(16,3)$

The largest possible number of vertices in a graph of maximum degree $16$ and diameter at most $3$.

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: $1055$ Checked construction
  degree-diameter-16-3-lower-1055, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 1985 Lower bound: $1600$
  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]
• 2026-09 Lower bound: $1920$
  Ryosuke Mizuno in September 2026
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]