Geodesic
On Borderenergetic graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017), p. 9

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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.
Classification : 05C50, 05C90
Keywords: energy (of graph), borderenergetic graph, hyperenergetic graph, equienergetic graphs, spectrum (of graph) 
Ivan Gutman. On Borderenergetic graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017), p. 9 . http://geodesic.mathdoc.fr/item/BASS_2017_42_a1/
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