Degree-diameter problem $N(15,10)$
The largest possible number of vertices in a graph of maximum degree $15$ and diameter at most $10$.
Lower bound:
$16021302724$
(16,021,302,724)
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: $10012349898$
(10,012,349,898)
Loz, E., & Sirán, J. (2008). New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics, 41, 63.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10-30
Lower bound: $16021302724$
(16,021,302,724)
Rajiv, R. (2026). New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts. Zenodo.
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]