Degree-diameter problem $N(5,3)$

The largest possible number of vertices in a graph of maximum degree $5$ and diameter at most $3$.

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: $54$ Checked construction
  degree-diameter-5-3-lower-54, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 2001-05-25 Lower bound: $72$
  Exoo, G. (2001). A family of graphs and the degree/diameter problem. Journal of Graph Theory, 37(2), 118-124.