The trivalent polyhedra on v vertices can be classified according to the maximal point-group symmetries of their graphs. A sum rule based on early work by Tutte relates the numbers, ni, of isomers belonging to groups with gi symmetry operations to an analytical function of the vertex count, giving a useful check on isomer enumeration and symmetry assignment.
P. W. Fowler and D. Mitchell, J. Chem. Soc., Faraday Trans., 1996, 92, 4145 DOI: 10.1039/FT9969204145
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