Degree-diameter problem $N(12,6)$
The largest possible number of vertices in a graph of maximum degree $12$ and diameter at most $6$.
Lower bound:
$364032$
(364,032)
Upper bound:
Unknown
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
-
2006-07-15
Lower bound: $359772$
(359,772)
Pineda-Villavicencio, G., Gómez, J., Miller, M., & Pérez-Rosés, H. (2006). New largest graphs of diameter 6: (Extended Abstract). Electronic Notes in Discrete Mathematics, 24, 153-160.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $364032$
(364,032)
Dharunish Yugeswardeenoo in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]