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 A191595 Order of smallest n-regular graph of girth 5. 7
 5, 10, 19, 30, 40, 50 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 18 15:26 EDT 2019. Contains 325143 sequences. (Running on oeis4.)