Geodesic
Graph Energies and Their Applications
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019), p. 29 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The energy $E(G)$ of a graph $G$ is the sum of absolute values of the eigenvalues of the adjacency matrix of $G$. This spectral quantity was introduced in 1978 by Ivan Gutman, but its extensive research started only twenty five years later. A large number (over hundred) variants of graph energy have been proposed, based on matrices other than the adjacency atrix. Research of these graph energies is nowadays very active, resulting in well over a thousand publications. In recent years, more than two papers on graph energies appear each week. Graph energies found a remarkable number of various applications. In this paper, we outline some basic, mainly statistical, facts on the research of graph energies, and point out their main applications.
Classification : 05C50, 05C90
Keywords: energy (of graph), spectrum (of graph), spectrum (of matrix), singular value (of matrix) 
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     author = {Ivan Gutman and Boris Furtula},
     title = {Graph {Energies} and {Their} {Applications}},
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Ivan Gutman; Boris Furtula. Graph Energies and Their Applications. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019), p. 29 . http://geodesic.mathdoc.fr/item/BASS_2019_44_a1/