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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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Graph Laplacian for image deblurring [PDF]
ETNA - Electronic Transactions on Numerical Analysis, 2021 Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variational ones are extremely popular. These approaches are characterized by substituting the original problem with a minimization one where the functional is composed of two terms ...
Bianchi D. +3 more
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Spektrum Laplace pada graf kincir angin berarah (Q_k^3)
Majalah Ilmiah Matematika dan Statistika, 2022 Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements ...
Melly Amaliyanah +2 more
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Graph Laplacian Mixture Model [PDF]
IEEE Transactions on Signal and Information Processing over Networks, 2020 Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in settings where all available data relate to the same graph.
Hermina Petric Maretic, Pascal Frossard
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A study on determination of some graphs by Laplacian and signless Laplacian permanental polynomials
AKCE International Journal of Graphs and Combinatorics, 2023 The permanent of an n × n matrix [Formula: see text] is defined as [Formula: see text] where the sum is taken over all permutations σ of [Formula: see text] The permanental polynomial of M, denoted by [Formula: see text] is [Formula: see text] where In ...
Aqib Khan +2 more
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Laplacian Fractional Revival on Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs.
Chan, Ada +5 more
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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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On Laplacian Equienergetic Signed Graphs [PDF]
Journal of Mathematics, 2021 The Laplacian energy of a signed graph is defined as the sum of the distance of its Laplacian eigenvalues from its average degree. Two signed graphs of the same order are said to be Laplacian equienergetic if their Laplacian energies are equal. In this paper, we present several infinite families of Laplacian equienergetic signed graphs.
Qingyun Tao, Lixin Tao
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COUPLE GRAPH BASED LABEL PROPAGATION METHOD FOR HYPERSPECTRAL REMOTE SENSING DATA CLASSIFICATION [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2018 Graph based semi-supervised classification method are widely used for hyperspectral image classification. We present a couple graph based label propagation method, which contains both the adjacency graph and the similar graph. We propose to construct the
X. P. Wang, Y. Hu, J. Chen
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Hodge Laplacians on Graphs [PDF]
SIAM Review, 2020 This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including cohomology and Hodge theory. The main feature of our approach is simplicity, requiring only knowledge of linear algebra and graph theory.
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