Degree-diameter problem $N(9,5)$

The largest possible number of vertices in a graph of maximum degree $9$ and diameter at most $5$.

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: None yet
• Upper bound: None yet

Updates from the literature

• 2008 Lower bound: $8200$
  Loz, E., & Sirán, J. (2008). New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics, 41, 63.
  [via The Degree Diameter Problem for General Graphs - Combinatorics Wiki]
• 2012-12-11 Lower bound: $8268$
  Canale, E., & Rodríguez, A. (2012). On the application of voltage graphs to the degree/diameter problem.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 2026-10 Lower bound: $9020$
  Nishant Bhakar in October 2026
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]