Construction of planar graphs for IPR fullerenes using 5- and 6-fold rotational symmetry: some eigenspectral analysis

Abstract

An algorithm has been developed for the construction of planar graphs for two series of IPR fullerenes of the general formula C_50 + 10n and C_60 + 12n (n = 1, 2, 3,…) maintaining 5- and 6-fold rotational symmetry, respectively. Some important utilities of these graphs have been shown. Simple rules have then been developed for factorising these graphs in order to obtain the eigenvalues corresponding to the totally symmetric irreducible representations of the C₅ and C₆ subgroups of the full point groups of fullerenes.