Cage order $n(19,7)$
The order of a $(19,7)$-cage, a $19$-regular graph of girth $7$ with the fewest possible vertices.
Lower bound:
$6518$
Verified
(not in the literature)
Upper bound:
Unknown
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:
$6518$
Lean proof
cage-19-7-lower-6518, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
No updates recorded.