Results 1 to 10 of about 41,978 (137)
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
doaj +5 more sources
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.
europepmc +6 more sources
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
doaj +4 more sources
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
doaj +4 more sources
Computing Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs [PDF]
The Electronic Journal of Linear Algebra, 2022 The Laplacian-energy-like invariant and the Kirchhoff index of an $n$-vertex simple connected graph $G$ are, respectively, defined to be $LEL(G)=\sum_{i=1}^{n-1}\sqrt{\mu_i}$ and $Kf(G)=n\sum_{i=1}^{n-1}\frac{1}{\mu_i}$, where $\mu_1,\mu_2,\ldots,\mu_{n-1},\mu_n=0$ are the Laplacian eigenvalues of $G$.
Sandeep Bhatnagar +2 more
semanticscholar +5 more sources
Remarks on "Comparison between the Laplacian energy-like invariant and the Kirchhoff index''
Acta Universitatis Sapientiae, Informatica, 2022 Abstract Let G be a simple connected graph of order n and size m. The matrix L(G)= D(G)− A(G) is called the Laplacian matrix of the graph G,where D(G) and A(G) are the degree diagonal matrix and the adjacency matrix, respectively.
Xiaodan Chen, Guoliang Hao
semanticscholar +5 more sources
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.
semanticscholar +4 more sources
Asymptotic Laplacian-energy-like invariant of lattices [PDF]
Applied Mathematics and Computation, 2015 6 pages, 2 ...
Jia‐Bao Liu +3 more
semanticscholar +6 more sources
Comparison between Laplacian--energy--like invariant and Kirchhoff index
The Electronic Journal of Linear Algebra, 2016 For a simple connected graph G of order n, having Laplacian eigenvalues μ_1, μ_2, . . . ,μ_{nâ1}, μ_n = 0, the Laplacianâenergyâlike invariant (LEL) and the Kirchhoff index (Kf) are defined as LEL(G) = \sum_{i=1}^{n-1} \sqrt{μ_i} Kf(G) = \sum_{i=1}^{n-1} 1/μ_i, respectively.
S. Pirzada, Hilal A. Ganie, İvan Gutman
semanticscholar +4 more sources
On Laplacian-energy-like invariant of a graph
Linear Algebra and its Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weizhong Wang, Yanfeng Luo
semanticscholar +5 more sources