cp's OEIS Frontend

A175847 Number of cyclically 4-connected simple cubic graphs on 2n vertices.

%I A175847 #43 Feb 06 2024 05:12:54
%S A175847 1,1,2,5,18,84,607,6100,78824,1195280,20297600,376940415,7565248679
%N A175847 Number of cyclically 4-connected simple cubic graphs on 2n vertices.
%C A175847 The (edge-)connected simple cubic graphs counted in A002851 can be classified as 1-connected (containing bridges), 2-connected, and 3-connected. The 3-connected graphs are subdivided in the cases (i) allowing a cut of 3 edges which leaves subgraphs with cycles and (ii) cyclically 4-connected and counted here. (Computed by adding the rows with k>=4 in Brouder's Table 1.)
%C A175847 Each of the non-isomorphic cyclically 4-connected graphs defines a 3n-j symbol of the vector coupling coefficients in the quantum mechanics of SO(3), one 6j symbol, one 9j symbol, two 12j symbols, five 15j symbols etc.
%C A175847 The Yutsis graphs (A111916) are a subset of the cyclically 4-connected graphs, which admit a representation as vertex-induced binary trees.
%C A175847 The value a(8)=576 is found in some earlier literature (e.g., Durr et al.) - _R. J. Mathar_, Sep 06 2011
%D A175847 A. P. Yutsis, I. B. Levinson, V. V. Vanagas, A. Sen, Mathematical apparatus of the theory of angular momentum, (1962).
%H A175847 G. Brinkmann, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199610)23:2&lt;139::AID-JGT5&gt;3.0.CO;2-U">Fast generation of cubic graphs</a>, Journal of Graph Theory, 23(2):139-149, 1996.
%H A175847 Gunnar Brinkmann, Jan Goedgebeur, Jonas Hagglund and Klas Markstrom, <a href="http://arxiv.org/abs/1206.6690">Generation and properties of snarks</a>, arXiv:1206.6690 [math.CO], 2012-2013.
%H A175847 B. Brinkmann, J. Goedgebeur and B. D. McKay, <a href="https://doi.org/10.46298/dmtcs.551">Generation of cubic graphs</a>, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.
%H A175847 Christian Brouder and Gunnar Brinkmann, <a href="http://dx.doi.org/10.1016/S0368-2048(97)00057-1">Theo Thole and the graphical methods</a>, J. Electr. Spectr. Relat. Phen. 86 (1-3) (1997) 127-132.
%H A175847 H. P. Dürr and F. Wagner, <a href="http://dx.doi.org/10.1007/BF02824938">Graphical methods for the execution of the gamma or sigma-algebra in spinor theories</a>, Nuov. Cim. 53A (1) (1968) 255.
%H A175847 J.-N. Massot, E. El-Baz and J. Lafoucrière, <a href="http://dx.doi.org/10.1103/RevModPhys.39.288">A general graphical method for angular momentum</a>, Rev. Mod. Phys. 39 (2) (1967) 288-305.
%H A175847 M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2&lt;137::AID-JGT7&gt;3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146.
%H A175847 Wikipedia, <a href="http://en.wikipedia.org/wiki/Table_of_simple_cubic_graphs">Table of simple cubic graphs</a>.
%e A175847 On 4 vertices we have a(2)=1, the tetrahedron.
%e A175847 On 6 vertices we count K_4 as a(3)=1, but not the utility graph.
%Y A175847 The labeled graphs in this class are counted by A007101. - _Brendan McKay_, Sep 23 2010
%K A175847 nonn,more
%O A175847 2,3
%A A175847 _R. J. Mathar_, Sep 26 2010
%E A175847 Extended by _Nico Van Cleemput_, Jan 26 2014