Geodesic
Graphs with extremal energy should have a small number of distinct eigenvalues
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 32 (2007) no. 1.

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

The sum of the absolute values of the eigenvalues of a graph is called the energy of the graph. We study the problem of finding graphs with extremal energy within specified classes of graphs. We develop tools for treating such problems and obtain some partial results. Using calculus, we show that an extremal graph ``should'' have a small number of distinct eigenvalues. However, we also present data that show in many cases that extremal graphs can have a large number of distinct eigenvalues. 
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     author = {D. Cvetkovi\'c and J. Grout},
     title = {Graphs with extremal energy should have a small number of distinct eigenvalues},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {43 - 57},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2007},
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D. Cvetković; J. Grout. Graphs with extremal energy should have a small number of distinct eigenvalues. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 32 (2007) no. 1. http://geodesic.mathdoc.fr/item/BASS_2007_32_1_a3/