Toroidal fullerenes with the Cayley graph structures

We classify all possible structures of fullerene Cayley graphs. We give each one a geometric model and compute the spectra of its finite quotients. Moreover, we give a quick and simple estimation for a given toroidal fullerene. Finally, we provide a realization of those families in three-dimensional space. (C) 2011 Elsevier B.V. All rights reserved.