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A014378 Number of connected regular graphs of degree 8 with n nodes. 21

%I #40 Dec 05 2022 11:01:07

%S 1,0,0,0,0,0,0,0,0,1,1,6,94,10786,3459386,1470293676,733351105935,

%T 423187422492342,281341168330848873,214755319657939505395,

%U 187549729101764460261498,186685399408147545744203815,210977245260028917322933154987

%N Number of connected regular graphs of degree 8 with n nodes.

%C Since the nontrivial 8-regular graph with the least number of vertices is K_9, there are no disconnected 8-regular graphs with less than 18 vertices. Thus for n<18 this sequence is identical to A180260. - _Jason Kimberley_, Sep 25 2009 and Feb 10 2011

%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/ConnectedGraph.html">Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OcticGraph.html">Octic Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RegularGraph.html">Regular Graph</a>

%F a(n) = A184983(n) + A181154(n).

%F a(n) = A180260(n) + A165878(n).

%F This sequence is the inverse Euler transformation of A180260.

%e a(0)=1 because the null graph (with no vertices) is vacuously 8-regular and connected.

%Y Contribution (almost all) from _Jason Kimberley_, Feb 10 2011: (Start)

%Y 8-regular simple graphs: this sequence (connected), A165878 (disconnected), A180260 (not necessarily connected).

%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), this sequence (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).

%Y Connected 8-regular simple graphs with girth at least g: A184981 (triangle); chosen g: A014378 (g=3), A181154 (g=4).

%Y Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3). (End)

%K nonn,hard

%O 0,12

%A _N. J. A. Sloane_

%E Using the symmetry of A051031, a(15) and a(16) were appended by _Jason Kimberley_, Sep 25 2009

%E a(17)-a(22) from _Andrew Howroyd_, Mar 13 2020

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)