Cage order $n(18,10)$
The order of a $(18,10)$-cage, a $18$-regular graph of girth $10$ with the fewest possible vertices.
Lower bound:
$177482$
(177,482)
Verified
(not in the literature)
Upper bound:
Unknown
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:
$177482$
(177,482)
Lean proof
cage-18-10-lower-177482, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
No updates recorded.