Geodesic
The Estrada Index
Zbornik radova, Tome 13 (2009) no. 21, p. 123

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If $\lambda_i,\;\;i=1,2,\ldots,n$, are the eigenvalues of the graph $G$, then the Estrada index $EE$ of $G$ is the sum of the terms $e^{\lambda_i}$. This graph invariant appeared for the first time in year 2000, in a paper by Ernesto Estrada, dealing with the folding of protein molecules. Since then a remarkable variety of other chemical and non-chemical applications of $EE$ were communicated. The mathematical studies of the Estrada index started only a few years ago. Until now a number of lower and upper bounds were obtained, and the problem of extremal $EE$ for trees solved. Also, approximations and correlations for $EE$ were put forward, valid for chemically interesting molecular graphs. In this paper the relevant results on the Estrada index are surveyed.
Classification : 05C50 05C90 92E10
Keywords: Estrada index, spectrum (of graph), chemistry 
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Hanyuan Deng; Slavko Radenković; Ivan Gutman. The Estrada Index. Zbornik radova, Tome 13 (2009) no. 21, p. 123 . http://geodesic.mathdoc.fr/item/ZR_2009_13_21_a5/