Cage order $n(19,13)$

The order of a $(19,13)$-cage, a $19$-regular graph of girth $13$ with the fewest possible vertices.

Lower bound: $38013662$ (38,013,662) 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.

Lower bound: $38013662$ (38,013,662) Lean proof
cage-19-13-lower-38013662, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

No updates recorded.