Cage order $n(19,5)$
The order of a $(19,5)$-cage, a $19$-regular graph of girth $5$ with the fewest possible vertices.
Lower bound:
$364$
Upper bound:
$512$
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:
$362$
Lean proof
cage-19-5-lower-362, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $512$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $364$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]