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Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions. [PDF]
Springerplus, 2016 Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity.
Liu JB, Cao J, Hayat T, Alsaadi FE.
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On two energy-like invariants of line graphs and related graph operations [PDF]
Journal of Inequalities and Applications, 2016 For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\mu_{1}\geq\mu_{2}\geq\cdots\geq\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\geq q_{2}\geq\cdots\geq q_{n}\geq0$ be its signless Laplacian eigenvalues.
Xiaodan Chen, Yaoping Hou, Jingjian Li
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Some observations on the Laplacian-energy-like invariant of trees [PDF]
Discrete Mathematics Letters, 2022 Summary: Let \(G\) be a graph of order \(n\). Denote by \(A\) the adjacency matrix of \(G\) and by \(D=\mathrm{diag}(d_1, \dots, d_n)\) the diagonal matrix of vertex degrees of \(G\). The Laplacian matrix of \(G\) is defined as \(L=D - A\). Let \(\mu_1, \mu_2,\cdots, \mu_{n-1}, \mu_n\) be eigenvalues of \(L\) satisfying \(\mu_1\geq \mu_2\geq \dots \geq
Marjan Matejić +3 more
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On Laplacian-energy-like invariant and incidence energy [PDF]
International Journal of Group Theory, 2015 For a simple connected graph G with n -vertices having Laplacian eigenvalues μ 1 , μ 2 , … , μ n−1 , μ n =0 , and signless Laplacian eigenvalues q 1 ,q 2 ,…,q n , the Laplacian-energy-like invariant(LEL ) and the incidence energy ...
Shariefuddin Pirzada , Hilal A. Ganie
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On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-11/μi and LEL(G)=Σi=1n-1
Emina Milovanovic +2 more
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On the Laplacian-energy-like invariant
Linear Algebra and its Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Das, Kinkar Ch. +2 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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(Generalized) Incidence and Laplacian-Like Energies
Journal of Mathematics, 2023 In this study, for graph Γ with r connected components (also for connected nonbipartite and connected bipartite graphs) and a real number ε≠0,1, we found generalized and improved bounds for the sum of ε-th powers of Laplacian and signless Laplacian ...
A. Dilek Maden, Mohammad Tariq Rahim
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The Laplacian-Energy-Like Invariants of Three Types of Lattices [PDF]
Journal of Analytical Methods in Chemistry, 2016 This paper mainly studies the Laplacian-energy-like invariants of the modified hexagonal lattice, modified Union Jack lattice, and honeycomb lattice. By utilizing the tensor product of matrices and the diagonalization of block circulant matrices, we derive closed-form formulas expressing the Laplacian-energy-like invariants of these lattices.
Zheng-Qing Chu, Jia-Bao Liu, Xiao-Xin Li
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NORMALIZED LAPLACIAN ENERGY AND NORMALIZED LAPLACIAN-ENERGY-LIKE INVARIANT OF SOME DERIVED GRAPHS
Matematički Vesnik, 2022 Summary: For a connected graph \(G\), the smallest normalized Laplacian eigenvalue is 0 while all others are positive and the largest cannot exceed the value 2. The sum of absolute deviations of the eigenvalues from 1 is called the normalized Laplacian energy, denoted by \(\mathbb{LE}(G)\).
Amin, Ruhul, Abu Nayeem, Sk. Md.
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