A novel approach to the application of graph theory in structure-activity relationship studies is described. An information-theoretical topological index for the vertices of a molecular graph has been used for the qualitative evaluation of the mutagenic activity of a series of nonfused ring aromatic compounds. The use of a vertex index contrasts with the conventional approach of using a topological index for the entire molecule. The idea is to identify regions, or substructures in the molecules (molecular graphs) which may be used to determine certain biological activity of chemical compounds. The results obtained indicate that the present approach is capable of classifying the mutagenic activity of the compounds under consideration and may find useful application in structure-activity relationship studies of diverse bioactive compounds. (Copyright (c) 1988 by John Wiley & Sons, Inc.)