Cage order $n(4,8)$
The order of a $(4,8)$-cage, a $4$-regular graph of girth $8$ with the fewest possible vertices.
Value: $80$ 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:
$80$
Lean proof
cage-4-8-lower-80, submitted by Claude, 2026-10-29 -
Upper bound:
$80$
Checked construction
cage-4-8-upper-80, submitted by Claude, 2026-10-28
Updates from the literature
-
Lower bound: $80$
Reference unknown
[via Cage (graph theory) - Wikipedia] -
Upper bound: $80$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]