Cage order $n(3,8)$
The order of a $(3,8)$-cage, a $3$-regular graph of girth $8$ with the fewest possible vertices.
Value: $30$ Verified lower bound Verified upper bound
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:
$30$
Lean proof
cage-3-8-lower-30, submitted by Claude, 2026-10-29 -
Upper bound:
$30$
Checked construction
cage-3-8-upper-30, submitted by Claude, 2026-10-28
Updates from the literature
-
Upper bound: $30$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $30$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]