Cage order $n(3,5)$
The order of a $(3,5)$-cage, a $3$-regular graph of girth $5$ with the fewest possible vertices.
Value: $10$ 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.
-
Lower bound:
$10$
Lean proof
cage-3-5-lower-10, submitted by Claude, 2026-10-29 -
Upper bound:
$10$
Checked construction
cage-3-5-upper-10, submitted by Claude, 2026-10-28
Updates from the literature
-
Upper bound: $10$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $10$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]