The Energy of a Graph: Old and New Results

By Ivan Gutman. 2001

720 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/cc0c5d8652aaf9a61b382104cdfa4a88a583db0a

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

Randic Matrix and Randic Energy (2010, background): “It should be noted that Theorem 4 is just the Randić–energy variant of the classical McClelland inequality [18–20].”
DISTANCE SPECTRA AND DISTANCE ENERGIES OF ITERATED LINE GRAPHS OF REGULAR GRAPHS (2009, background): “[19], and was conceived in full analogy with the ordinary graph energy E(G), defined as [12, 13, 14]”
On the energy of some circulant graphs (2006, background): “This notion is related to some applications of graph theory to chemistry and has been studied intensively in the literature, see [1,3,5,6,9–12,15,17] and references therein.”
Graph energy change due to edge deletion (2008, background): “[7] See Theorem 4.2 for a sufﬁcient condition that E (G − { e } ) E (G) .”
Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index (2010, background): “The energy E = E(G) of a graph G is, by definition, equal to the sum of absolute values of the eigenvalues of this graph [5, 6, 18, 23, 27, 28].”
THE NORMALIZED LAPLACIAN MATRIX AND GENERAL RANDI C INDEX OF GRAPHS (2010, background): “the energy [30], Laplacian energy [32], signless Laplacian energy, distance energy [54] and incidence energy [31] of a graph have received much interest.”
On the Harary Energy and Harary Estrada Index of a Graph (2010, methodology): “In the second section of this paper, by considering the papers [13, 14, 16, 23], we will adapt the works on distance energy to introduce and study on Harary energy.”
On Laplacian-energy-like invariant of a graph < (2012, background): “Various properties of graph energy may be found in [5,8].”
Sharp bounds on the distance spectral radius and the distance energy of graphs (2009, background): “This definition was motivated by the much older [4] and nowadays extensively studied [5–7,10–12,14,15] graph energy, defined in a manner fully analogous to Eq.”
On the distance spectra of some graphs (2008, background): “This definition was motivated by the much older [7] and nowadays extensively studied [8, 9, 10, 13, 14, 15, 16] graph energy, defined in a manner fully analogous to Eq.”
Extremal Matching Energy of Bicyclic Graphs (2013, positive): “For details see the new book on graph energy [18] and the reviews [8, 10].”
Unicyclic graphs with maximal energy (2002, background): “One of the long-known results in this field is the Coulson integral formula (see [7,8]):”
Estimating the Estrada index (2007, background): “Among connected graphs of a given order the star has the minimum energy [9].”
A note on energy of some graphs (2008, background): “The properties of E(G) are discussed in detail in [6, 8, 9].”
Note on the energy of regular graphs (2009, background): “For more information on graph energy we refer to [5, 6], and for terminology and notations not defined here, we refer to Bondy and Murty [2].”
The Laplacian-energy Like Invariant is an Energy Like Invariant (2010, background): “For details on the mathematical aspects of the theory of graph energy see the reviews [10, 11] and the references cited therein.”