Degree-diameter problem $N(18,9)$
The largest possible number of vertices in a graph of maximum degree $18$ and diameter at most $9$.
Lower bound:
$6645271633$
(6,645,271,633)
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
-
2010-09
Lower bound: $5768971167$
(5,768,971,167)
Loz, E., & Pineda-Villavicencio, G. (2010). New benchmarks for large-scale networks with given maximum degree and diameter. The Computer Journal, 53(7), 1092-1105.
[via The Degree Diameter Problem for General Graphs - Combinatorics Wiki] -
2026-10-30
Lower bound: $6645271633$
(6,645,271,633)
Rajiv, R. (2026). New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts. Zenodo.