Cage order $n(7,5)$
Uzyel, via Wikimedia Commons. CC BY-SA 3.0.
The order of a $(7,5)$-cage, a $7$-regular graph of girth $5$ with the fewest possible vertices.
Value: $50$ Verified lower bound Verified upper bound
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:
$50$
Lean proof
cage-7-5-lower-50, submitted by Claude, 2026-10-29 -
Upper bound:
$50$
Checked construction
cage-7-5-upper-50, submitted by Claude, 2026-10-28
Updates from the literature
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Upper bound: $50$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $50$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]