Geodesic
Bounds on the Distance Laplacian Energy of Graphs
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 245 .

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 simple connected graph, $v_i$ its vertex, and $D_i$ the sum of distances between $v_i$ and the other vertices of $G$. Let $\delta_1, \delta_2,\ldots, \delta_n$ be the eigenvalues of the distance matrix $\mathbf D$ of $G$, and $\delta^L_1,\delta^L_2,\ldots,\delta^L_n$ the eigenvalues of the distance Laplacian matrix $\mathbf D^L$ of $G$. An earlier much studied quantity $E_D(G)=\sum_{i=1}^n|\delta_i|$ is the distance energy. We now define the distance Laplacian energy as $LE_D(G)=\sum_{i=1}^n \left|\delta_i^L-\frac{1}{n} um_{i=1}^n D_i \right|$, and obtain bounds for it.
Classification : 05C50 05C35 15A18
Keywords: Distance (in graph), Distance Laplacian matrix, Distance Laplacian energy 
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     author = {Jieshan Yang and Lihua You and Ivan Gutman},
     title = {Bounds on the {Distance} {Laplacian} {Energy} of {Graphs}},
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Jieshan Yang; Lihua You; Ivan Gutman. Bounds on the Distance Laplacian Energy of Graphs. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 245 . http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a3/