Note Added In Proof. Another method for symmetry perception (atoms only) came to our knowledge recently: Davis, M. I.; Ellzey, M. L., Jr. J . Comput. Chem. 1983, 4,
267.ACKNOWLEDGMENT We thank Prof. M. Randie for information on endospectral graphs and on the Cayley-Hamilton theorem and Dr. A. Bomelburg (IBM Deutschland) for a useful programming hint. REFERENCES AND NOTES ( I ) Riicker, G.; Rucker, Ch. Chimia, in press. (2) Shelley, C. A.; Munk, M. E. (7) Balaban, A. T.; Mekenyan, 0.; Bonchev, D. J . Comput. Chem. 1985, 6, 538, and references cited therein. (8) Bersohn, M. Comput. Chem. 1987, 11, 67. (9) Ihlenfeldt, W. D.; Gasteiger, J. In Software-Entwicklung in der Chernie 2; Gasteiger, J.; Ed.; Springer-Verlag: Berlin, 1988; pp 13-33. (IO) Gray, N. A. B. Computer-assisted structure elucidation; Wiley: New York, 1986; Chapter 9.( I I ) For the kind of symmetry discussed in this paper (which is clearly not the usual geometric symmetry in three-dimensional space) the terms "constitutional symmetry" and 'topological symmetry" have both been used in the literature2-s since the information contained in the constitution (not configuration or conformation) is considered exclusively; Le., geometric properties like bond lengths and angles or cis/trans relationships are disregarded. However, the term topological symmetry may be misunderstood since topological isomers [as defined earlier, e.g., a simple macrocycle and its knotted isomer (Frisch, H. L.; Wasserman, E. J . Am. Chem. SOC. 1961.83, 3789) or the pair 28/29 in Figure 31 are indistinguishable in terms of the symmetry under discussion here