Degree-diameter problem $N(4,4)$
The largest possible number of vertices in a graph of maximum degree $4$ and diameter at most $4$.
Lower bound:
$104$
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:
$84$
Checked construction
degree-diameter-4-4-lower-84, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
-
2001-05-25
Lower bound: $96$
Exoo, G. (2001). A family of graphs and the degree/diameter problem. Journal of Graph Theory, 37(2), 118-124. -
2001-06
Lower bound: $98$
Geoffrey Exoo, after May 2001 (i.e. after https://doi.org/10.1002/jgt.1007)
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-08
Lower bound: $104$
Nishant Bhakar in August 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]