Cage order $n(18,12)$
The order of a $(18,12)$-cage, a $18$-regular graph of girth $12$ with the fewest possible vertices.
Value: $3017196$ (3,017,196) Verified lower bound (not in the literature)
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.
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Lower bound:
$3017196$
(3,017,196)
Lean proof
cage-18-12-lower-3017196, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $3017196$
(3,017,196)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]