Degree-diameter problem $N(3,8)$
The largest possible number of vertices in a graph of maximum degree $3$ and diameter at most $8$.
Lower bound:
$360$
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:
$272$
Checked construction
degree-diameter-3-8-lower-272, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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2001-05-25
Lower bound: $330$
Exoo, G. (2001). A family of graphs and the degree/diameter problem. Journal of Graph Theory, 37(2), 118-124. -
2018
Lower bound: $360$
Jianxiang Chen, 2018
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]