A191595 Order of smallest n-regular graph of girth 5.

5, 10, 19, 30, 40, 50

Offset

2,1

Comments

Current upper bounds for a(8)..a(20) are 80, 96, 124, 154, 203, 230, 288, 312, 336, 448, 480, 512, 576. - Corrected from "Lower" to "Upper" and updated, from Table 4 of the Dynamic cage survey, by Jason Kimberley, Dec 29 2012

Current lower bounds for a(8)..a(20) are 67, 86, 103, 124, 147, 174, 199, 230, 259, 294, 327, 364, 403. - from Table 4 of the Dynamic cage survey via Jason Kimberley, Dec 31 2012

Links

Table of n, a(n) for n=2..7.

M. Abreu et al., A family of regular graphs of girth 5, Discrete Math., 308 (2008), 1810-1815.

Andries E. Brouwer, Cages

Geoff Exoo, Regular graphs of given degree and girth

G. Exoo and R. Jajcay, Dynamic cage survey, Electr. J. Combin. (2008, 2011).

G. Royle, Cages of higher valency

Formula

a(n) >= A002522(n) with equality if and only if n = 2, 3, 7 or possibly 57. - Jason Kimberley, Nov 02 2011

Crossrefs

Orders of cages: A054760 (n,k), A000066 (3,n), A037233 (4,n), A218553 (5,n), A218554 (6,n), A218555 (7,n), this sequence (n,5).

Moore lower bound on the orders of (k,g) cages: A198300 (square); rows: A000027 (k=2), A027383 (k=3), A062318 (k=4), A061547 (k=5), A198306(k=6), A198307 (k=7), A198308 (k=8), A198309 (k=9), A198310 (k=10),A094626 (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), A188377 (g=7). - Jason Kimberley, Nov 02 2011

Sequence in context: A134467 A178132 A227844 * A047882 A184260 A053311

Adjacent sequences: A191592 A191593 A191594 * A191596 A191597 A191598

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Jun 07 2011

Extensions

a(2) = 5 prepended by Jason Kimberley, Jan 02 2013

Status

approved