Totally symmetric Kekulé structures in fullerene graphs with ten or more symmetries
نویسندگان
چکیده
(Received May 2, 2012) Graph theoretic fullerenes are designed to model large carbon molecules: each vertex represents a carbon atom and the edges represent chemical bonds. A totally symmetric Kekulé structure in a fullerene is a set of independent edges which is fixed by all symmetries of the fullerene. It was suggested in a paper by S.J.Austin, J.Baker, P.W.Fowler, D.E.Manolopoulos and in a paper by K.M. Rogers and P.W.Fowler that molecules with totally symmetric Kekulé structures could have special physical and chemical properties. Starting from a catalog given by J.E.Graver, we study all graph theoretic fullerenes with at least ten symmetries and we establish exactly which of them have at least one totally symmetric Kekulé structure.
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