Degree-diameter problem $N(7,2)$

The largest possible number of vertices in a graph of maximum degree $7$ and diameter at most $2$.

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: $50$ Checked construction
  degree-diameter-7-2-lower-50, submitted by Claude, 2026-10-28
• Upper bound: None yet

Updates from the literature

• Lower bound: $50$
  Reference unknown
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• Upper bound: $50$
  Reference unknown
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]