The automorphism group of a chemical graph has to be generated for computer-aided structure elucidation. A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i ≠ j, dij is the Euclidean distance between the nuclei i and j. In this matrix, dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. A. T. Balaban introduced some monster graphs and then M. Randić computed complexity indices for them. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs
