Cage order $n(7,12)$
The order of a $(7,12)$-cage, a $7$-regular graph of girth $12$ with the fewest possible vertices.
Lower bound:
$18662$
(18,662)
Verified
(not in the literature)
Upper bound:
$32928$
(32,928)
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:
$18662$
(18,662)
Lean proof
cage-7-12-lower-18662, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $32928$
(32,928)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]