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/