A number of molecular systems which have identical graph spectra have been examined. It was found that in some instances a pair of isospectral graphs forms a basis for generation of a family of structurally related isospectral pairs, while in other instances the production of other related systems is not possible. A theorem is stated which characterizes the former class of “fertile” isospectral pairs. It is shown that isospectral systems, although a rather special class of structures, are not uncommon and that several molecules of interest in chemistry have isospectral “mates”.
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Randić et al. (1976) studied this question.