Cage order $n(9,11)$
The order of a $(9,11)$-cage, a $9$-regular graph of girth $11$ with the fewest possible vertices.
Lower bound:
$42130$
(42,130)
Verified
(not in the literature)
Upper bound:
$74752$
(74,752)
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:
$42130$
(42,130)
Lean proof
cage-9-11-lower-42130, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
2010
Upper bound: $74752$
(74,752)
G. Araujo-Pardo, On upper bounds of odd girth cages, Discrete Math. 310 (2010) 1622-1626.
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]