Cage order $n(3,10)$

Koko90, via Wikimedia Commons. CC BY-SA 3.0.

The order of a $(3,10)$-cage, a $3$-regular graph of girth $10$ with the fewest possible vertices.

Value: $70$

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: $62$ Lean proof
cage-3-10-lower-62, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

Upper bound: $70$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]
Lower bound: $70$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]