Relating Estrada index with spectral radius

The Estrada index EE is a recently proposed molecular structure-descrip- tor, used in the modeling of certain features of the 3D structure of organic mole- cules, in particular of the degree of folding of proteins and other long-chain biopo- lymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigen- value) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.

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