Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry

摘要

Threefold rotational symmetry has been used to develop an algorithm for the construction of planar graphs of IPR fullerenes and to factorize their characteristic polynomials. Two series of fullerenes of the formula C60+12n and C60+18n have thus been obtained. The algorithm has been shown to be useful for predicting the nature of variation of the point groups of the fullerenes with increased n, for counting the number of C-13 nuclear magnetic resonance (NMR) signals (along with their relative intensities), and also for obtaining a large part of their eigenspectra. (c) 2005 Wiley Periodicals, Inc.