Geodesic
Bounds for the distance energy of a graph
Kragujevac Journal of Mathematics, Tome 31 (2008) no. 1

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The distance energy of a graph $G$ is defined as the sum of the absolute values of the eigenvalues of the distance matrix of $G$. Recently bounds for the distance energy of a graph of diameter 2 were determined. In this paper we obtain bounds for the distance energy of any connected graph $G$ , thus generalizing the earlier results. 
@article{KJM_2008_31_1_a5,
     author = {Harishchandra S. Ramane and Deepak S. Revankar and Ivan Gutman and Siddani Bhaskara Rao and B. Devadas Acharya and Hanumappa B. Walikar},
     title = {Bounds for the distance energy of a graph},
     journal = {Kragujevac Journal of Mathematics},
     pages = {59 - 68},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2008},
     zbl = {1199.05239},
     url = {http://geodesic.mathdoc.fr/item/KJM_2008_31_1_a5/}
}
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Harishchandra S. Ramane; Deepak S. Revankar; Ivan Gutman; Siddani Bhaskara Rao; B. Devadas Acharya; Hanumappa B. Walikar. Bounds for the distance energy of a graph. Kragujevac Journal of Mathematics, Tome 31 (2008) no. 1. http://geodesic.mathdoc.fr/item/KJM_2008_31_1_a5/