Degree-diameter problem $N(6,2)$

The largest possible number of vertices in a graph of maximum degree $6$ 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: $32$ Checked construction
  degree-diameter-6-2-lower-32, submitted by Claude, 2026-11-02
  [construction from McKay, B. D., Miller, M., & Širáň, J. (1998). A note on large graphs of diameter two and given maximum degree. Journal of Combinatorial Theory, Series B, 74(1), 110-118.]
• Upper bound: None yet

Updates from the literature

• 1977 Lower bound: $32$
  Wegner, G. (1977). Graphs with given diameter and a coloring problem.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 2006 Upper bound: $32$
  Molodtsov, S. G. (2006). Largest graphs of diameter 2 and maximum degree 6. General Theory of Information Transfer and Combinatorics, 853-857.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]