Geodesic
On second-stage spectrum and energy of a graph
Kragujevac Journal of Mathematics, Tome 34 (2010) no. 1 
Singaraj K. Ayyaswamy; Selvaraj Balachandran; Ivan Gutman. On second-stage spectrum and energy of a graph. Kragujevac Journal of Mathematics, Tome 34 (2010) no. 1. http://geodesic.mathdoc.fr/item/KJM_2010_34_1_a11/
@article{KJM_2010_34_1_a11,
     author = {Singaraj K. Ayyaswamy and Selvaraj Balachandran and Ivan Gutman},
     title = {On second-stage spectrum and energy of a graph},
     journal = {Kragujevac Journal of Mathematics},
     pages = {139 - 146},
     year = {2010},
     volume = {34},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/KJM_2010_34_1_a11/}
}
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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 simple graph. The {t derived graph\/} of $G$, denoted by $G^\dagger$, is the graph having the same vertex set as $G$, in which two vertices are adjacent if and only if their distance in $G$ is two. We establish several spectral properties of $G^\dagger$, including its energy.