Cage order $n(5,8)$
The order of a $(5,8)$-cage, a $5$-regular graph of girth $8$ with the fewest possible vertices.
Value: $170$ 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:
$170$
Lean proof
cage-5-8-lower-170, submitted by Claude, 2026-10-29 -
Upper bound:
$170$
Checked construction
cage-5-8-upper-170, submitted by Claude, 2026-10-28
Updates from the literature
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Lower bound: $170$
Reference unknown
[via Cage (graph theory) - Wikipedia] -
Upper bound: $170$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]