Computing symmetry of fullerene molecule C84

Suppose M is a molecule and G is its molecular graph with atoms labeled by numbers 1, 2, ... n. Define the adjacency matrix A = [a(ij)] of G to be a 0-1 matrix with this property that a(ij) = 1 if and only if the there is a bond connecting atoms i and j. An Euclidean graph associated to M is defined by a weighted graph with the adjacency matrix D = [d(ij)], where for i # j d(ij) is the Euclidean distance between the nuclei i and j. In this matrix d(ii) can be taken as zero if all the nuclei are equivalent. In this work a 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 the fullerenes molecule C-84.