Abstract
A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√2m/n)+a2, where a1 ≈ 1.098 and a2 = −0.64 are empirically determined fitting constants. Within classes of benzenoid isomers (which all have equal n and m), the Estrada index is linearly proportional to the number of bay regions.
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