Cage order $n(17,5)$
The order of a $(17,5)$-cage, a $17$-regular graph of girth $5$ with the fewest possible vertices.
Lower bound:
$294$
Upper bound:
$448$
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:
$290$
Lean proof
cage-17-5-lower-290, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $448$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $294$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]