Laplacian matrix
LAPLACIAN MATRIX IN ALGEBRAIC GRAPH THEORY
... We have shown how graphs can be converted into pattern vectors by utilizing the spectral decomposition of the Laplacian matrix and basis sets of symmetric polynomials. These feature vectors are complete, ...
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Computing the additive degree-Kirchhoff index with the Laplacian matrix
... modified Laplacian matrix can be written exclusively in terms of the Laplacian matrix: indeed, the matrix D is the diagonal matrix whose elements are those in the diagonal of L ...
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Unsupervised software defect prediction using median absolute deviation threshold based spectral classifier on signed Laplacian matrix
... adjacency matrix and the absolute of adjacency matrix using ...signed Laplacian matrix in Eq. 9 from the absolute of adjacency matrix in step ...signed Laplacian matrix is ...
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Seidel Signless Laplacian Energy of Graphs
... the Laplacian matrix is changed into D(G) + A(G), then interesting and non-trivial spectral properties are ...signless Laplacian spectra has been developed ...
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The Signless Laplacian Estrada Index of Unicyclic Graphs
... signless Laplacian matrix (among all graphs with given numbers of vertices and edges) is an important prob- lem in the spectral graph theory (see [10, 11, ...signless Laplacian matrix can be ...
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Bounds for the signless Laplacian energy of digraphs
... skew Laplacian matrix of a digraph contains the information of the degree of vertices and it is a skew symmetric ...the Laplacian energy of undirected graphs, Adiga and Khoshbakht [2] gave the skew ...
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Laplacian Energy of a Fuzzy Graph
... such matrix, adjacency matrix is called the spectrum of the ...adjacency matrix of . The Laplacian spectrum of the graph , consisting of the numbers { , … , } , is the spectrum of its ...
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On Eccentricity Version of Laplacian Energy of a Graph
... 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 matrix of G and average ...
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The Bounds for Eigenvalues of Normalized Laplacian Matrices and Signless Laplacian Matrices
... In this paper, we found extreme eigenvalues of normalized Laplacian matrix and signless Laplacian matrix of a G graph with using theirs traces... Conjugate transpose of A denoted by A∗.[r] ...
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On the Laplacian spectral characterization of $\Pi$ shape trees
... degree matrix of G. The graph matrix M is called the adjacency matrix, the Laplacian matrix and the signless Laplacian matrix of G if M equals A(G), L(G) = D − A(G) and ...
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Laplacian Support Vector Machines Trained in the Primal
... pirically evaluated to be significantly smaller than n, without the need of storing in memory the Hessian matrix and its inverse. Training times are significantly reduced on all selected benchmarks, in particular, ...
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Existence of Solutions for the -Laplacian Problem with Singular Term
... After Kov´aˇcik and R´akosn´ ık first discussed the L px Ω spaces and W k,px Ω spaces in 1, a lot of research has been done concerning these kinds of variable exponent spaces, for example, see 2–5 for the properties of ...
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Existence results for classes of -Laplacian semipositone equations
... Shivaji, Existence and uniqueness for a class of quasilinear elliptic boundary value problems, Journal of Di ff erential Equations 193 (2003), no.. Shivaji, Di ff usive logistic equation w[r] ...
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Multiplicity for fractional differential equations with p-Laplacian
... It is quite natural to study fractional differential equation relative to equation. Re- cently, many scholars have paid more attention to the fractional order differential equation boundary value problems with ...
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Existence of a positive solution for a-Laplacian semipositone problem
... Shivaji, An existence result on positive solutions for a class of p-Laplacian systems , Nonlinear Anal.. Shivaji, Existence results for classes of p-Laplacian semipositone equations , su[r] ...
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Global bifurcation results for general Laplacian problems
... general Laplacian pro- blems [3,7,8], but most of them are about j = ψ ...general Laplacian problem (P) and prove the existence and multipli- city result for ...
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Harmonicity of horizontally conformal maps and spectrum of the Laplacian
... We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if φ : M → N is a horizontally conformal map such that the tension field is divergence ...
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Conformal variations of the spectral zeta function of the Laplacian
... notions of the determinant of the Laplacian and Casimir energy are defined via the spectral zeta function, see e.g [24, 9, 21, 8, 10, 23, 7, 15, 25] and [3] among other literature. Various generalisations of the ...
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Geometric structure of graph Laplacian embeddings
... graph Laplacian also has N connected components and its first N eigenvectors coincide with rescaled versions of the indicator functions of the N connected components of M restricted to M n ...resulting ...
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On Second-Order Differential Equations with Nonhomogeneous -Laplacian
... Equation with general nonhomogeneous Φ-Laplacian, including classical and singular Φ- Laplacian, is investigated. Necessary and su ffi cient conditions for the existence of nonoscillatory solutions satisfying ...
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