Results 11 to 20 of about 79,461 (254)
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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A special class of triple starlike trees characterized by Laplacian spectrum
AIMS Mathematics, 2021 Two graphs are said to be cospectral with respect to the Laplacian matrix if they have the same Laplacian spectrum. A graph is said to be determined by the Laplacian spectrum if there is no other non-isomorphic graph with the same Laplacian spectrum.
10.3934/math.2021260 +4 more
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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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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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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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Normalized Laplacians for gain graphs
American Journal of Combinatorics, 2022 We propose the notion of normalized Laplacian matrix \(\mathcal{L}(\Phi)\) for a gain graph \(\Phi\) and study its properties in detail, providing insights and counterexamples along the way. We establish bounds for the eigenvalues of \(\mathcal{L}(\Phi)\) and characterize the classes of graphs for which equality holds.
M. Rajesh Kannan +2 more
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Acta Scientiarum: Technology, 2023 Spectral Graph theory has been utilized frequently in the field of Computer Vision and Pattern Recognition to address challenges in the field of Image Segmentation and Image Classification.
Subramaniam Usha +3 more
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Mathematics, 2021 Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in
Jichao Ma +3 more
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
wiley +1 more source
Incremental eigenpair computation for graph Laplacian matrices: theory and applications [PDF]
, 2017 The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications, the number of clusters or communities (say,
Al Hasan, Mohammad +2 more
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