Cage order $n(9,7)$

The order of a $(9,7)$-cage, a $9$-regular graph of girth $7$ with the fewest possible vertices.

Lower bound: $658$ Verified (not in the literature)
Upper bound: $1152$

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: $658$ Lean proof
cage-9-7-lower-658, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

2010 Upper bound: $1152$
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]