We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph. © 2007 Elsevier B.V. All rights reserved
Let G be a graph with m edges and let ρ be the largest eigenvalue of its adjacency matrix. It is sho...
Our first aim in this note is to prove some inequalities relating the eigenvalues of a Hermitian mat...
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of...
We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient: In pa...
AbstractIn this note we discuss interlacing inequalities relating the eigenvalues of a partitioned H...
In this note we discuss interlacing inequalities relating the eigenvalues of a partitioned Hermitian...
We give several old and some new applications of eigenvalue interlacing to matrices associated to gr...
We give several old and some new applications of eigenvalue interlacing to matrices associated to gr...
AbstractWe give several old and some new applications of eigenvalue interlacing to matrices associat...
AbstractWe first give a result on eigenvalues of the line graph of a graph. We then use the result t...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
Abstract In 1993 Hong asked what are the best bounds on the k\u27th largest eigenvalue λk(G) of a gr...
AbstractIn this paper, we first obtain a sharp upper bound for the eigenvalues of the adjacency matr...
AbstractLet G be a graph on vertex set V=v1,v2,…,vn. Let di be the degree of vi, let Ni be the set o...
AbstractA new proof of the complete interlacing theorem for singular values is presented. The techni...
Let G be a graph with m edges and let ρ be the largest eigenvalue of its adjacency matrix. It is sho...
Our first aim in this note is to prove some inequalities relating the eigenvalues of a Hermitian mat...
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of...
We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient: In pa...
AbstractIn this note we discuss interlacing inequalities relating the eigenvalues of a partitioned H...
In this note we discuss interlacing inequalities relating the eigenvalues of a partitioned Hermitian...
We give several old and some new applications of eigenvalue interlacing to matrices associated to gr...
We give several old and some new applications of eigenvalue interlacing to matrices associated to gr...
AbstractWe give several old and some new applications of eigenvalue interlacing to matrices associat...
AbstractWe first give a result on eigenvalues of the line graph of a graph. We then use the result t...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
Abstract In 1993 Hong asked what are the best bounds on the k\u27th largest eigenvalue λk(G) of a gr...
AbstractIn this paper, we first obtain a sharp upper bound for the eigenvalues of the adjacency matr...
AbstractLet G be a graph on vertex set V=v1,v2,…,vn. Let di be the degree of vi, let Ni be the set o...
AbstractA new proof of the complete interlacing theorem for singular values is presented. The techni...
Let G be a graph with m edges and let ρ be the largest eigenvalue of its adjacency matrix. It is sho...
Our first aim in this note is to prove some inequalities relating the eigenvalues of a Hermitian mat...
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of...
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