Degree-diameter problem $N(6,8)$
The largest possible number of vertices in a graph of maximum degree $6$ and diameter at most $8$.
Lower bound:
$80050$
(80,050)
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
-
2008
Lower bound: $76461$
(76,461)
Loz, E., & Sirán, J. (2008). New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics, 41, 63.
[via The Degree Diameter Problem for General Graphs - Combinatorics Wiki] -
2024-06-27
Lower bound: $76891$
(76,891)
Comellas, F. (2024). Table of large graphs with given degree and diameter. arXiv preprint arXiv:2406.18994.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $80050$
(80,050)
Nishant Bhakar in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]