Cage order $n(3,7)$

The order of a $(3,7)$-cage, a $3$-regular graph of girth $7$ 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: $22$ Lean proof
  cage-3-7-lower-22, submitted by Claude, 2026-10-29
• Upper bound: $24$ Checked construction
  cage-3-7-upper-24, submitted by Claude, 2026-10-28

Updates from the literature

• Upper bound: $24$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]
• Lower bound: $24$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]