Cage order $n(8,3)$
The order of a $(8,3)$-cage, a $8$-regular graph of girth $3$ with the fewest possible vertices.
Value: $9$ Verified lower bound (not in the literature) Verified upper bound (not in the literature)
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:
$9$
Lean proof
cage-8-3-lower-9, submitted by Claude, 2026-10-29 -
Upper bound:
$9$
Checked construction
cage-8-3-upper-9, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.