Degree-diameter problem $N(6,4)$

The largest possible number of vertices in a graph of maximum degree $6$ and diameter at most $4$.

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: $355$ Checked construction
  degree-diameter-6-4-lower-355, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 2001-05-25 Lower bound: $380$
  Exoo, G. (2001). A family of graphs and the degree/diameter problem. Journal of Graph Theory, 37(2), 118-124.
• 2008 Lower bound: $390$
  Loz, E., & Sirán, J. (2008). New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics, 41, 63.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 2026-09-24 Lower bound: $441$
  Rajiv, R. (2026). New lower bounds for the degree-diameter problem from Cayley graphs, orbit graphs and lifts. Zenodo.
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]