Geodesic
Relations between Kirchhoff index and Laplacian–energy–like invariant
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 37 (2012) no. 1 
B. Arsić; I. Gutman; K. Ch. Das; K. Xu. Relations between Kirchhoff index and Laplacian–energy–like invariant. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 37 (2012) no. 1. http://geodesic.mathdoc.fr/item/BASS_2012_37_1_a3/
@article{BASS_2012_37_1_a3,
     author = {B. Arsi\'c and I. Gutman and K. Ch. Das and K. Xu},
     title = {Relations between {Kirchhoff} index and {Laplacian{\textendash}energy{\textendash}like} invariant},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {59 - 70},
     year = {2012},
     volume = {37},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BASS_2012_37_1_a3/}
}
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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

The Kirchhoff index Kf and the Laplacian–energy– like invariant LEL are two graph invariants defined in terms of the Laplacian eigenvalues. If $\mu_1 \ge\mu_2 \ge...\mu_{n-1} > \mu_n=0$ are the Laplacian eigenvalues of a connected n-vertex graph, then $ Kf = \sum{i=1}{n-1}\frac{1}{\mu_i}$ and $LEL = um{i=1}{n-1}qrt{\mu_i}$. We examine the conditions under which Kf > LEL. Among other results we show that Kf > LEL holds for all trees, unicyclic, bicyclic, tricyclic, and tetracyclic connected graphs, except for a finite number of graphs. These exceptional graphs are determined.