Laplacian energy of a graph

By Ivan Gutman, Bo Zhou. 2006

559 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/184153a6dc8002cf38b271d9ee96c2274226b54f

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

ON SPECTRAL MOMENTS AND ENERGY OF GRAPHS (2007, background): “Of the numerous papers on graph energy that recently appeared, we quote here only a few [7–29].”
The von Neumann Entropy of Networks (2008, background): “Notably, graph-states and spin networks, just to mention two major ones: graph-states are certain quantum error correcting codes, important for characterizing the computational resources in measurement based quantum computation [6, 19]; spin networks are arrangements of interacting quantum…”
On the sum of the Laplacian eigenvalues of a tree (2011, unknown): “In a similar direction, Zhou [14] has considered the sum of powers of the Laplacian eigenvalues of a graph.”
Energy of a Graph (2006, unknown): “Gutman and Zhou [5] defined the Laplacian energy of a graph using its Laplacian matrix D − A, where A is the adjacency matrix and D is the diagonal matrix of degrees: LE(G) = n ∑”
On the normalized Laplacian energy and general Randić index R-1 of graphs (2010, background): “Recently, the adjacency energy [9], Laplacian energy [11], signless Laplacian energy, distance energy [21] and incidence energy [10] of a graph has received much interest.”
Minimum energy on trees with k pendent vertices (2006, unknown): “, see, [1,3,5–10,12–23,25–27,29–34]).”
On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n (2021, background): “Gutman and Zhou [22] defined the Laplacian energy of G as LE(G) = n ∑ i=1 ∣∣∣∣µi − 2mn ∣∣∣∣.”
On sum of powers of the Laplacian eigenvalues of graphs (2008, methodology): “Recall that the energy of a graph is equal to the sum of the absolute values of its ordinary eigenvalues [3] and that an energy – like quantity was proposed and studied in [7] based on the Laplacian eigenvalues.”
The Laplacian-energy Like Invariant is an Energy Like Invariant (2010, background): “In an attempt to provide a Laplacian–spectral analogue of the graph energy, two of the present authors proposed the so-called Laplacian energy , defined as [12, 13]”