Geodesic
Note on Estrada and $L$-Estrada indices of graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 34 (2009) no. 1 
G. H. Fath-Tabar; A. R. Ashrafi; I. Gutman. Note on Estrada  and $L$-Estrada indices of graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 34 (2009) no. 1. http://geodesic.mathdoc.fr/item/BASS_2009_34_1_a0/
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     author = {G. H. Fath-Tabar and A. R. Ashrafi and I. Gutman},
     title = {Note on {Estrada}  and $L${-Estrada} indices of graphs},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {1 - 16},
     year = {2009},
     volume = {34},
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a graph of order $n$\,. Let $\lambda_1,\lambda_2,\ldots,\lambda_n$ be its eigenvalues and $\mu_1,\mu_2,\ldots,\mu_n$ its Laplacian eigenvalues. The Estrada index $EE$ of the graph $G$ is defined as the sum of the terms $e^{\lambda_i} \ , \ i=1,2,\ldots,n$\,. In this paper the notion of Laplacian--Estrada index ($L$-Estrada index, $LEE$) of a graph is introduced. It is defined as the sum of the terms $e^{\mu_i} \ , i=1,2,łdots,n$\,. The basic properties of $LEE$ are established, and compared with the analogous properties of $EE$\,. In addition, the Estrada and $L$-Estrada indices of some important classes of graphs are computed.