Degree-diameter problem $N(20,2)$

The largest possible number of vertices in a graph of maximum degree $20$ 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: $381$ Checked construction
  degree-diameter-20-2-lower-381, submitted by Claude, 2026-10-28
  [construction from Brown, W. G. (1966).]
• Upper bound: None yet

Updates from the literature

• 1966 Lower bound: $381$
  Brown, W. G. (1966).
  [via The Degree Diameter Problem for General Graphs - Combinatorics Wiki]