On Laplacian-energy-like invariant of a graph <

By Weizhong Wang, Yanfeng Luo. 2012

77 citations recorded by the source corpus.

Abstract Let G be a simple graph of order n , and let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 be the Laplacian spectrum of G . The Laplacian-energy-like invariant of G ( LEL for short) is defined as LEL ( G ) = ∑ i = 1 n - 1 μ i . In this paper, a new lower bound for LEL of graphs in terms of the maximum degree is given. Meanwhile, an upper bound and a lower bound for LEL of the line graph (resp., the subdivision graph and the total graph) of a regular graph G are obtained.

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

View Paper: https://www.semanticscholar.org/paper/7177b614825ad56cd0787c28afd8e1728a743b9a

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

The Laplacian-energy Like Invariant is an Energy Like Invariant (2010, background): “Liu and Liu [30] named LEL “Laplacian–energy like”, which gives the impression that it was expected to be similar to LE .”
ON LAPLACIAN LIKE ENERGY OF TREES (2011, background): “This concept was introduced in [6] where it was shown that it has similar features as molecular graph energy [7] (for recent results on graph energy see [8]).”
Linear Algebra and its Applications (2010, background): “This leads to a time-continuous, semi-discrete problem in the form of an initial-value problem for a system of ordinary differential equations (ODEs).”
Extreme Atom-Bond Connectivity Index of Graphs (2011, background): “, see [5,8-10]) and several of them have found applications in QSPR/QSAR studies.”