3n-j Symbols
The 6-j symbol is the first representative, n=2, of 3n-j symbols that are defined as sums of products of n of Wigner's 3-jm coefficients. The sums are over all combinations of m that the 3n j-coefficients admit, i.e., which lead to non-vanishing contributions.
If each 3-jm factor is represented by a vertex and each j by an edge, these 3n-j symbols can be mapped on certain 3-regular graphs with 3n vertices and 2n nodes. The 6-j symbol is associated with the K4 graph on 4 vertices, the 9-j symbol with the utility graph on 6 vertices, and the two different (non-isomorphic) 12-j symbols with the Q_3 and Wagner graphs on 8 vertices. Symmetry relations are generally representative of the automorphism group of these graphs.
Read more about this topic: 9-j Symbol
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