Isospectral Benzenoid Derivatives

FIGURE 3.6 Isospectral pair 1,4-divynilbenzene and 2-phenylbutadiene have common fragment vinylbenzene, the two endospectral vertices are shown as small circles. 

FIGURE 3.7 Endospectral graphs having from n = 9 to n = 12 vertices, having one, two, and three branching vertices. The endsopectral vertices are indicated by small circles. 

To several researchers, including us, the note from Heilbronner and Jones appeared as an unwarranted dramatization and misrepresentation of the irrelevance of graph spectra in chemistry. Thus, one of the present authors has sent to the 

A few short historical comments may clarify the sitnation. One should recall that the notion of isospectral systems originated in physics with the question Can one hear the shape of a drum which was the title of a paper by Mark Kac [74] in 1966 in the American Mathematical Monthly of the Mathematical Association of America. Kac had been invited to submit an article that bronght interesting mathematical 

Before leaving HMO, let us mention an important theorem about HMO energies for alternant systems (% electron systems having no odd rings) due to Coulson and Rushbrooke [90], known as the Coulson-Rushbrooke pairing theorem  

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