Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/15030
 Title: Laplacian spread of graphs: lower bounds and relations with invariant parameters Author: Andrade, EnideCardoso, DomingosRobbiano, MariaRodriguez, Jonnathan Keywords: Spectral Graph TheoryMatrix spreadLaplacian Spread Issue Date: 1-Dec-2015 Publisher: Elsevier Abstract: The spread of an $n\times n$ complex matrix $B$ with eigenvalues $\beta _{1},\beta _{2},\ldots ,\beta _{n}$ is defined by \begin{equation*} s\left( B\right) =\max_{i,j}\left\vert \beta _{i}-\beta _{j}\right\vert , \end{equation*}% where the maximum is taken over all pairs of eigenvalues of $B$. Let $G$ be a graph on $n$ vertices. The concept of Laplacian spread of $G$ is defined by the difference between the largest and the second smallest Laplacian eigenvalue of $G$. In this work, by combining old techniques of interlacing eigenvalues and rank $1$ perturbation matrices new lower bounds on the Laplacian spread of graphs are deduced, some of them involving invariant parameters of graphs, as it is the case of the bandwidth, independence number and vertex connectivity. Peer review: yes URI: http://hdl.handle.net/10773/15030 DOI: 10.1016/j.laa.2015.08.027 ISSN: 0024-3795 Appears in Collections: CIDMA - ArtigosOGTCG - Artigos

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