نتایج جستجو برای: seidel laplacian eigenvalues

تعداد نتایج: 31896  

2009
ART M. DUVAL CAROLINE J. KLIVANS

We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms of the eigenvalues of its cellular Laplacian operators, generalizing a previous result for simplicial complexes. As an application, we obtain explicit formulas for spanning tree enumerators and Laplacian eigenvalues of cubes; the latter are integers. We prove a weighted version of the eigenvalue formula, pr...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2009
Zhongzhi Zhang Yi Qi Shuigeng Zhou Yuan Lin Jihong Guan

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing ...

Journal: :Proceedings of the American Mathematical Society 2022

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian on graphs discuss its rigidity. As applications the eigenvalues, Lichnerowicz-type estimates some combinatorial for graphs.

2014
Zhengwei Wu Victor M. Preciado

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of ‘local’ subgraphs of the network. We call a subgraph local when it is induced by the set of nodes obtained from a breath-first search (BFS)...

2009
Jianxi Li Wai Chee Shiu An Chang

Let G = (V,E) be a graph without loops and multiple edges. Let n and m be the number of vertices and edges of G, respectively. Such a graph will be referred to as an (n,m)-graph. For v ∈ V (G), let d(v) be the degree of v. In this paper, we are concerned only with undirected simple graphs (loops and multiple edges are not allowed). Let G be a graph with n vertices and the adjacency matrix A(G)....

2014
NATHAN REFF

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

2017
Steve Butler

The problem of relating the eigenvalues of the normalized Laplacian for a weighted graph G and G − H, for H a subgraph of G is considered. It is shown that these eigenvalues interlace and that the tightness of the interlacing is dependent on the number of nonisolated vertices of H. Weak coverings of a weighted graph are also defined and interlacing results for the normalized Laplacian for such ...

2007
STEVE BUTLER Stephen J. Kirkland

The problem of relating the eigenvalues of the normalized Laplacian for a weighted graph G and G − H, for H a subgraph of G is considered. It is shown that these eigenvalues interlace and that the tightness of the interlacing is dependent on the number of nonisolated vertices of H. Weak coverings of a weighted graph are also defined and interlacing results for the normalized Laplacian for such ...

Journal: :Discussiones Mathematicae Graph Theory 2015
Clive Elphick Pawel Wocjan

One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenva...

2011
JAMES P. KELLIHER

We show that the k-th eigenvalue of the Dirichlet Laplacian is strictly less than the k-th eigenvalue of the classical Stokes operator (equivalently, of the clamped buckling plate problem) for a bounded domain in the plane having a locally Lipschitz boundary. For a C boundary, we show that eigenvalues of the Stokes operator with Navier slip (friction) boundary conditions interpolate continuousl...

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