Degree-diameter problem $N(7,4)$

The largest possible number of vertices in a graph of maximum degree $7$ 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: $602$ Checked construction
  degree-diameter-7-4-lower-602, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 1997 Lower bound: $672$
  Sampels, M. (1997). Large networks with small diameter. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 2026-10 Lower bound: $684$
  Michel de Messieres in October 2026
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]