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Title: Laplacian spread of graphs: lower bounds and relations with invariant parameters
Author: Andrade, Enide
Cardoso, Domingos
Robbiano, Maria
Rodriguez, Jonnathan
Keywords: Spectral Graph Theory
Matrix spread
Laplacian 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
DOI: 10.1016/j.laa.2015.08.027
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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