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The Laplacian Spectrum of a Graph II [PDF]

SIAM Journal on Discrete Mathematics, 1994
Summary: [For Part I see \textit{R. Grone}, \textit{R. Merris} and \textit{V. S. Sunder}, SIAM J. Matrix Anal. Appl. 11, No. 2, 218-238 (1990; Zbl 0733.05060).] Let \(G\) be a graph. Denote by \(D(G)\) the diagonal matrix of its vertex degrees and by \(A(G)\) its adjacency matrix. Then \(L(G) = D(G) -A(G)\) is the Laplacian matrix of \(G\).
Robert Grone, Russell Merris
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Laplacian Dynamics on General Graphs

Bulletin of Mathematical Biology, 2013
In previous work, we have introduced a "linear framework" for time-scale separation in biochemical systems, which is based on a labelled, directed graph, G, and an associated linear differential equation, dx/dt = L(G) ∙ x, where L(G) is the Laplacian matrix of G. Biochemical nonlinearity is encoded in the graph labels. Many central results in molecular
Mirzaev, Inomzhon, Gunawardena, Jeremy
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On the Laplacian energy of a graph

Czechoslovak Mathematical Journal, 2006
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Conjugate Laplacian matrices of a graph

Discrete Mathematics, Algorithms and Applications, 2018
Let [Formula: see text] be a simple graph of order [Formula: see text] Let [Formula: see text] and [Formula: see text] where [Formula: see text] and [Formula: see text] are two nonzero integers and [Formula: see text] is a positive integer such that [Formula: see text] is not a perfect square. In [M.
BÜYÜKKÖSE, ŞERİFE, Kabatas, Ulkunur
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Graph Embeddings and Laplacian Eigenvalues

SIAM Journal on Matrix Analysis and Applications, 2000
Summary: Graph embeddings are useful in bounding the smallest nontrivial eigenvalues of Laplacian matrices from below. For an \(n \times n\) Laplacian, these embedding methods can be characterized as follows: The lower bound is based on a clique embedding into the underlying graph of the Laplacian. An embedding can be represented by a matrix \(\Gamma\);
Stephen Guattery, Gary L. Miller
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Laplacian Controllability for Graphs with Integral Laplacian Spectrum

Mediterranean Journal of Mathematics, 2021
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The Laplacian spread of line graphs

Discrete Mathematics, 2023
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Jianbin Zhang, Yinglin Wu, Jianping Li
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Graphs and Laplacians

2017
In this chapter, we are interested in exploring questions such as the following. If a group G acts on a graph \(\Gamma \), what is the relationship between the spectrum of \(\Gamma \) and the spectrum of the quotient \(\Gamma /G\)?
W. David Joyner, Caroline Grant Melles
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The Laplacian of a Graph

2001
The Laplacian is another important matrix associated with a graph, and the Laplacian spectrum is the spectrum of this matrix. We will consider the relationship between structural properties of a graph and the Laplacian spectrum, in a similar fashion to the spectral graph theory of previous chapters. We will meet Kirchhoff’s expression for the number of
Chris Godsil, Gordon Royle
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Bayesian spiked Laplacian graphs

J. Mach. Learn. Res., 2023
Summary: In network analysis, it is common to work with a collection of graphs that exhibit heterogeneity. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify communities, and graph Laplacian-based methods are routinely used.
Leo L. Duan, George Michailidis, Mingzhou Ding   +2 more
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