OFFSET
2,3
COMMENTS
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.)
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.
The Yutsis graphs (A111916) are a subset of the cyclically 4-connected graphs, which admit a representation as vertex-induced binary trees.
The value a(8)=576 is found in some earlier literature (e.g., Durr et al.) - R. J. Mathar, Sep 06 2011
REFERENCES
A. P. Yutsis, I. B. Levinson, V. V. Vanagas, A. Sen, Mathematical apparatus of the theory of angular momentum, (1962).
LINKS
G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.
Gunnar Brinkmann, Jan Goedgebeur, Jonas Hagglund and Klas Markstrom, Generation and properties of snarks, arXiv:1206.6690 [math.CO], 2012-2013.
B. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.
Christian Brouder and Gunnar Brinkmann, Theo Thole and the graphical methods, J. Electr. Spectr. Relat. Phen. 86 (1-3) (1997) 127-132.
H. P. Dürr and F. Wagner, Graphical methods for the execution of the gamma or sigma-algebra in spinor theories, Nuov. Cim. 53A (1) (1968) 255.
J.-N. Massot, E. El-Baz and J. Lafoucrière, A general graphical method for angular momentum, Rev. Mod. Phys. 39 (2) (1967) 288-305.
M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.
Wikipedia, Table of simple cubic graphs.
EXAMPLE
On 4 vertices we have a(2)=1, the tetrahedron.
On 6 vertices we count K_4 as a(3)=1, but not the utility graph.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, Sep 26 2010
EXTENSIONS
Extended by Nico Van Cleemput, Jan 26 2014
STATUS
approved