Eigenvalues of the Laplacian of a graph[J].Linear and Multilinear Algebra,1985.141-145.W.N. Anderson, T.D. Morley, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra 18 (1985) 141-145.W N Ander
Eigenvalues of the Laplacian of a graph[J].Linear and Multilinear Algebra,1985.141-145.W.N. Anderson, T.D. Morley, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra 18 (1985) 141-145.Anderson W N,Morley T D.Eigenvalues of the Laplacian of a graph.Linear and ...
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been applied to several fields, such as randomized algorithms,...
On a Lower Bound for the Laplacian Eigenvalues of a GraphMathematics - Combinatorics05C50If $\\mu_m$ and $d_m$ denote, respectively, the $m$-th largest Laplacianeigenvalue and the $m$-th largest vertex degree of a graph, then $\\mu_m\\geqslant d_m-m+2$. This inequality was ...
Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d‾=2mn, clique number ω having Laplacian eigenvalues μ1,μ2,…,μn−1,μn=0. For k (1≤k≤n), let Sk(G)=∑i=1kμi and let σ (1≤σ≤n−1) be the number of Laplacian eigenvalue...
proposed the Szeged matrix and Laplacian Szeged matrix in [6]. Here we introduce another matrix of a graph. The adjacent matrix A(G)=[aij]n×n of G is the integer matrix with rows and columns indexed by its vertices, such that the ij-th-entry is equal to the number of edges ...
Laplacian eigenvalues of a graphSum of eigenvaluesLargest eigenvalueThe study of eigenvalues of graphs has a long history. Since the early days, representation theory and number theory have been very useful for examining the spectra of strongly regular graphs with symmetries. In contrast, recent ...
In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues...
本期专栏为 “谱图理论” 系列的第8期,将介绍耶鲁大学教授、两届哥德尔奖得主 Daniel A. Spielman 所著图书 《Spectral and Algebraic Graph Theory》(电子版链接) 第八章 Ch8: Eigenvalues of Random Graphs …
The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to weight-dependent walk. In this paper, we first present a study on the transition weight matrix of a weighted network....