Degree-diameter problem $N(6,5)$

The largest possible number of vertices in a graph of maximum degree $6$ 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: $1395$ Checked construction
  degree-diameter-6-5-lower-1395, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 2008 Lower bound: $1404$
  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]
• 2026-08-24 Lower bound: $1518$
  Rajiv, R. (2026). Improved lower bounds for the degree-diameter problem from metacyclic groups, coset graphs and affine lifts. Zenodo.
  [via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]