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Eigenvalues of weighted 𝑝-Laplacian [PDF]
Proceedings of the American Mathematical Society, 2013 In a paper by Z. Lu and J. Rowlett, it is shown that the eigenvalues of the weighted Laplacian can be approximated by eigenvalues of a naturally associated family of narrow graphs. In this paper, we generalize this result to the p p -Laplacian.
Lihan Wang
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Eigenvalues for systems of fractional $p$-Laplacians [PDF]
Rocky Mountain Journal of Mathematics, 2018 We study the eigenvalue problem for a system of fractional $p-$Laplacians, that is, $$ \begin{cases} (- _p)^r u = \dfrac p|u|^{ -2}u|v|^ &\text{in } ,\vspace{.1cm} (- _p)^s u = \dfrac p|u|^ |v|^{ -2}v &\text{in } , u=v=0 &\text{in } ^c=\R^N\setminus . \end{cases} $$ We show that there is a first (smallest) eigenvalue that
Leandro M. Del Pezzo, Julio D. Rossi
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Eigenvalues of the Laplacian on forms [PDF]
Proceedings of the American Mathematical Society, 1982 Some bounds for eigenvalues of the Laplace operator acting on forms on a compact Riemannian manifold are derived. In case of manifolds without boundary we give upper bounds in terms of the curvature, its covariant derivative and the injectivity radius.
Józef Dodziuk
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Graph toughness from Laplacian eigenvalues [PDF]
Algebraic Combinatorics, 2022 The toughness t(G) of a graph G=(V,E) is defined as t(G)=min|S| c(G-S), in which the minimum is taken over all S⊂V such that G-S is disconnected, where c(G-S) denotes the number of components of G-S. We present two tight lower bounds for t(G) in terms of the Laplacian eigenvalues and provide strong support for a conjecture for a better bound which, if ...
Gu, Xiaofeng, Haemers, Willem H.
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Monophonic Distance Laplacian Energy of Transformation Graphs Sn^++-,Sn^{+-+},Sn^{+++}
Ratio Mathematica, 2023 Let $G$ be a simple connected graph of order $n$, $v_{i}$ its vertex. Let $\delta^{L}_{1}, \delta^{L}_{2}, \ldots, \delta^{L}_{n}$ be the eigenvalues of the distance Laplacian matrix $D^{L}$ of $G$. The distance Laplacian energy is denoted by $LE_{D}(G)$.
Diana R, Binu Selin T
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On graphs with distance Laplacian eigenvalues of multiplicity n−4
AKCE International Journal of Graphs and Combinatorics, 2023 Let G be a connected simple graph with n vertices. The distance Laplacian matrix [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the diagonal matrix of vertex transmissions and [Formula: see text] is the distance ...
Saleem Khan, S. Pirzada, A. Somasundaram
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Distributed Solution of Laplacian Eigenvalue Problems [PDF]
SIAM Journal on Numerical Analysis, 2022 28 ...
Malinen, Jarmo +3 more
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On Eccentricity Version of Laplacian Energy of a Graph [PDF]
Mathematics Interdisciplinary Research, 2017 The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian
Nilanjan De
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Integral Laplacian graphs with a unique repeated Laplacian eigenvalue, I
Special Matrices, 2023 AbstractThe setSi,n={0,1,2,…,n−1,n}\{i}{S}_{i,n}=\left\{0,1,2,\ldots ,n-1,n\right\}\setminus \left\{i\right\},1⩽i⩽n1\leqslant i\leqslant n, is called Laplacian realizable if there exists an undirected simple graph whose Laplacian spectrum isSi,n{S}_{i,n}. The existence of such graphs was established by Fallat et al.
Hameed Abdul, Tyaglov Mikhail
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Bounds for Laplacian graph eigenvalues [PDF]
Mathematical Inequalities & Applications, 2012 Let G be a connected simple graph whose Laplacian eigenvalues are 0 = μn (G) μn−1 (G) · · · μ1 (G) . In this paper, we establish some upper and lower bounds for the algebraic connectivity and the largest Laplacian eigenvalue of G . Mathematics subject classification (2010): 05C50, 15A18.
Maden, A. Dilek, Buyukkose, Serife
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