Cage order $n(19,8)$
The order of a $(19,8)$-cage, a $19$-regular graph of girth $8$ with the fewest possible vertices.
Lower bound:
$12350$
(12,350)
Verified
(not in the literature)
Upper bound:
$13642$
(13,642)
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:
$12350$
(12,350)
Lean proof
cage-19-8-lower-12350, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $13642$
(13,642)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]