A191595 - OEIS

%I #34 Jul 31 2017 10:02:22

%S 5,10,19,30,40,50

%N Order of smallest n-regular graph of girth 5.

%C 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

%C 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

%H M. Abreu et al., <a href="http://dx.doi.org/10.1016/j.disc.2007.04.031">A family of regular graphs of girth 5</a>, Discrete Math., 308 (2008), 1810-1815.

%H Andries E. Brouwer, <a href="http://www.win.tue.nl/~aeb/graphs/cages/cages.html">Cages</a>

%H Geoff Exoo, <a href="http://ginger.indstate.edu/ge/CAGES">Regular graphs of given degree and girth</a>

%H G. Exoo and R. Jajcay, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS16">Dynamic cage survey</a>, Electr. J. Combin. (2008, 2011).

%H G. Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cages/allcages.html">Cages of higher valency</a>

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

%Y 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).

%Y 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

%K nonn,more,hard

%O 2,1

%A _N. J. A. Sloane_, Jun 07 2011

%E a(2) = 5 prepended by _Jason Kimberley_, Jan 02 2013