Degree-diameter problem $N(10,5)$
The largest possible number of vertices in a graph of maximum degree $10$ and diameter at most $5$.
Lower bound:
$33397$
(33,397)
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: $13140$
(13,140)
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: $13203$
(13,203)
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] -
2026-09-23
Lower bound: $33397$
(33,397)
Rajiv, R. (2026). Large graphs of diameter five from a duality of order four of the split Cayley hexagon H(9). Zenodo.
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]