Degree-diameter problem $N(3,2)$

The largest possible number of vertices in a graph of maximum degree $3$ 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: $10$ Checked construction
  degree-diameter-3-2-lower-10, submitted by Claude, 2026-10-28
• Upper bound: None yet

Updates from the literature

• Lower bound: $10$
  Reference unknown
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• Upper bound: $10$
  Reference unknown
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]