Degree-diameter problem $N(6,9)$
The largest possible number of vertices in a graph of maximum degree $6$ and diameter at most $9$.
Lower bound:
$331387$
(331,387)
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: $307845$
(307,845)
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] -
2012-12-11
Lower bound: $331387$
(331,387)
Canale, E., & Rodríguez, A. (2012). On the application of voltage graphs to the degree/diameter problem.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]