|
%I #39 Dec 05 2022 11:00:25
%S 1,0,0,0,0,1,9,88193,113314233813,281341168330848874,
%T 1251392240942040452186674,9854603833337765095207342173991,
%U 134283276101750327256393048776114352985
%N Number of connected regular graphs of degree 9 with 2n nodes.
%C Since the nontrivial 9-regular graph with the least number of vertices is K_10, there are no disconnected 9-regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9-regular graphs on 2n vertices. - _Jason Kimberley_, Sep 25 2009
%D CRC Handbook of Combinatorial Designs, 1996, p. 648.
%D I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>
%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RegularGraph.html">Regular Graph.</a>
%F a(n) = A184993(n) + A181170(n).
%e The null graph on 0 vertices is vacuously connected and 9-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Feb 10 2011
%Y Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), this sequence (k=9), A014382 (k=10), A014384 (k=11).
%Y 9-regular simple graphs: this sequence (connected), A185293 (disconnected).
%Y Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).
%Y Connected 9-regular simple graphs with girth exactly g: A184993 (g=3).
%K nonn,more,hard
%O 0,7
%A _N. J. A. Sloane_
%E a(8) appended using the symmetry of A051031 by _Jason Kimberley_, Sep 25 2009
%E a(9)-a(10) from _Andrew Howroyd_, Mar 13 2020
%E a(10) corrected and a(11)-a(12) from _Andrew Howroyd_, May 19 2020
| 