Geodesic
On Borderenergetic graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A graph $G$ of order $n$ is said to be borderenergetic if its energy is equal to $2n-2$ and if $G \not \cong K_n$. The first such graph was discovered in 2001, but their systematic study started only in 2015. The main hitherto established results on borderenergetic graphs are outlined, and a few new established. Borderenergetic graphs (of the same order) are mutually equienergetic. The difference in their structure indicates which structural features of a graph can vary, without affecting the value of its energy. In particular, it is shown that this applies to the number of edges. 
@article{BASS_2017_42_1_a1,
     author = {Ivan Gutman},
     title = {On {Borderenergetic} graphs},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {9 - 18},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a1/}
}
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Ivan Gutman. On Borderenergetic graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1. http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a1/