Calculation of the Symmetry of C24 Fullerene

Abstract

In this paper we present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C₂₄ fullerene. It is well known to associate an Euclidean graph to a molecule. Balasubramanian computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. It is also proved that algorithm, which is useful for finding symmetry of molecules. Using this algorithm, a new simple method is described, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of fullerene C₂₄.