Cage order $n(19,12)$
The order of a $(19,12)$-cage, a $19$-regular graph of girth $12$ with the fewest possible vertices.
Lower bound:
$4001438$
(4,001,438)
Verified
(not in the literature)
Upper bound:
$4938480$
(4,938,480)
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:
$4001438$
(4,001,438)
Lean proof
cage-19-12-lower-4001438, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $4938480$
(4,938,480)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]