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Estrada index of acyclic molecules

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2,...λn are the eigenvalues of the molecular graph, then EE = Σeλι In the case of trees with n vertices (that are the graph representations of alkane isomers C n H 2n+2 ), the main structural factor influencing the differences between the EE-values has been found to be the Zagreb index Zg. The coefficient b in the regression line EE = a Zg + b is an almost perfectly linear function of n, implying that in the case of alkanes, EE linearly increases with the number of carbon atoms.