Cage order $n(3,9)$

The order of a $(3,9)$-cage, a $3$-regular graph of girth $9$ 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: $46$ Lean proof
  cage-3-9-lower-46, submitted by Claude, 2026-10-29
• Upper bound: None yet

Updates from the literature

• Upper bound: $58$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]
• Lower bound: $58$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]