Estrada index of acyclic molecules

Abstract

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ₁, λ₂,..., λո are the eigenvalues of the molecular graph, then EE=Ʃeλi . In the case of trees with n vertices (that are the graph representations of alkane isomers CռH2ռ₊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.