Degree-diameter problem $N(13,2)$

The largest possible number of vertices in a graph of maximum degree $13$ 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: $162$ Checked construction
  degree-diameter-13-2-lower-162, 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

• 1998-09 Lower bound: $162$
  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.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]