Cage order $n(15,12)$
The order of a $(15,12)$-cage, a $15$-regular graph of girth $12$ with the fewest possible vertices.
Lower bound:
$1158390$
(1,158,390)
Verified
(not in the literature)
Upper bound:
$1957376$
(1,957,376)
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:
$1158390$
(1,158,390)
Lean proof
cage-15-12-lower-1158390, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $1957376$
(1,957,376)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]