Cage order $n(13,4)$
The order of a $(13,4)$-cage, a $13$-regular graph of girth $4$ with the fewest possible vertices.
Value: $26$ 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:
$26$
Lean proof
cage-13-4-lower-26, submitted by Claude, 2026-10-29 -
Upper bound:
$26$
Checked construction
cage-13-4-upper-26, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.