Degree-diameter problem $N(12,4)$

The largest possible number of vertices in a graph of maximum degree $12$ and diameter at most $4$.

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

• 1982 Lower bound: $4680$
  Bermond, J. C., Delorme, C., & Farhi, G. (1982). Large graphs with given degree and diameter III. In North-Holland Mathematics Studies (Vol. 62, pp. 23-31). North-Holland.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 2026-10 Lower bound: $6156$
  Nishant Bhakar in October 2026
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]