Cage order $n(9,8)$

The order of a $(9,8)$-cage, a $9$-regular graph of girth $8$ with the fewest possible vertices.

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: $1170$ Lean proof
  cage-9-8-lower-1170, submitted by Claude, 2026-10-29
• Upper bound: None yet

Updates from the literature

• Upper bound: $1170$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]