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Unicyclic graphs with equal Laplacian energy [PDF]
Linear and Multilinear Algebra, 2013 11 pages, 11 figures, slightly modified version of Theorem 1 when compared with original ...
Eliseu Fritscher +2 more
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Characterizing trees with large Laplacian energy
Linear Algebra and Its Applications, 2014 We investigate the problem of ordering trees according to their Laplacian energy. More precisely, given a positive integer $n$, we find a class of cardinality approximately $\sqrt{n}$ whose elements are the $n$-vertex trees with largest Laplacian energy.
Eliseu Fritscher +2 more
exaly +3 more sources
Some remarks on Laplacian eigenvalues and Laplacian energy of graphs
Mathematical Communications, 2010 Suppose $\mu_1$, $\mu_2$, ... , $\mu_n$ are Laplacian eigenvalues of a graph $G$. The Laplacian energy of $G$ is defined as $LE(G) = \sum_{i=1}^n|\mu_i - 2m/n|$. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of $K_n$ are presented.
Ashrafi, Ali Reza +1 more
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On Laplacian resolvent energy of graphs [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a simple connected graph of order $n$ and size $m$. The matrix $L(G)=D(G)-A(G)$ is the Laplacian matrix of $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix, respectively. For the graph $G$, let $d_{1}\geq d_{
Sandeep Bhatnagar +2 more
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Vertex weighted Laplacian Energy of union of graphs [PDF]
Computer Science Journal of Moldova, 2018 The vertex weighted Laplacian energy with respect to the vertex weight $w$ of a graph $G$ with $n$ vertices is defined as ~$LE_w(G)=\sum\limits_{i=1}^n|\mu_i-\bar{w}|$, where ${{\mu }_{1}},{{\mu }_{2}},...,{{\mu }_{n}}$ are the Laplacian eigenvalues of ...
Nilanjan De
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On a conjecture of Laplacian energy of trees [PDF]
Discrete Mathematics, Algorithms and Applications, 2021 Let [Formula: see text] be a simple graph with [Formula: see text] vertices, [Formula: see text] edges having Laplacian eigenvalues [Formula: see text]. The Laplacian energy LE[Formula: see text] is defined as LE[Formula: see text], where [Formula: see text] is the average degree of [Formula: see text]. Radenković and Gutman conjectured that among all
Hilal A. Ganie +2 more
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Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications
Axioms, 2021 The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research.
Siti Nurul Fitriah Mohamad +3 more
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Local Energy Estimates for the Fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2021 The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the ...
Juan Pablo Borthagaray +2 more
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Signless Laplacian energy, distance Laplacian energy and distance signless Laplacian spectrum of unitary addition Cayley graphs [PDF]
Linear and Multilinear Algebra, 2021 In this paper we compute bounds for signless Laplacian energy, distance signless Laplacian eigenvalues and signless Laplacian energy of unitary addition Cayley graph G_{n}. We also obtain distance Laplacian eigenvalues and distance Laplacian energy of G_{n}.
P., Naveen, A. V, Chithra
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