Cage order $n(18,9)$
The order of a $(18,9)$-cage, a $18$-regular graph of girth $9$ with the fewest possible vertices.
Lower bound:
$93961$
(93,961)
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.
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Lower bound:
$93961$
(93,961)
Lean proof
cage-18-9-lower-93961, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
No updates recorded.