Degree-diameter problem $N(15,2)$
The largest possible number of vertices in a graph of maximum degree $15$ and diameter at most $2$.
Lower bound:
$190$
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:
$183$
Checked construction
degree-diameter-15-2-lower-183, submitted by Claude, 2026-11-02
[construction from Brown, W. G. (1966).] - Upper bound: None yet
Updates from the literature
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2012
Lower bound: $187$
Eduardo A. Canale, 2012
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-09
Lower bound: $190$
Dharunish Yugeswardeenoo in September 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]