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A175847
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Number of cyclically 4-connected simple cubic graphs on 2n vertices.
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2
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1, 1, 2, 5, 18, 84, 607, 6100, 78824, 1195280, 20297600, 376940415, 7565248679
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OFFSET
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2,3
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COMMENTS
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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
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REFERENCES
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A. P. Yutsis, I. B. Levinson, V. V. Vanagas, A. Sen, Mathematical apparatus of the theory of angular momentum, (1962).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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