Cage order $n(12,3)$
The order of a $(12,3)$-cage, a $12$-regular graph of girth $3$ with the fewest possible vertices.
Value: $13$ 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:
$13$
Lean proof
cage-12-3-lower-13, submitted by Claude, 2026-10-29 -
Upper bound:
$13$
Checked construction
cage-12-3-upper-13, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.