On graphs with exactly one eigenvalue less than −1

Graphs with fourth Laplacian eigenvalue less than two

In this paper, all connected graphs with the fourth largest Laplacian eigenvalue less than two are determined, which are used to characterize all connected graphs with exactly three Laplacian eigenvalues no less than two. Moreover, we determine bipartite graphs such that the adjacency matrices of their line graphs have exactly three nonnegative eigenvalues. © 2003 Elsevier Ltd. All rights reser...

Graphs with three distinct eigenvalues and largest eigenvalue less than

Article history: Received 13 June 2008 Accepted 13 November 2008 Available online xxxx Submitted by R.A. Brualdi AMS classification: 05C50

Indefinite copositive matrices with exactly one positive eigenvalue or exactly one negative eigenvalue

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...

Ela Indefinite Copositive Matrices with Exactly One Positive Eigenvalue or Exactly One Negative Eigenvalue

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...

On symmetric matrices with exactly one positive eigenvalue