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Title: A lower bound for the energy of symmetric matrices and graphs
Author: Andrade, Enide
Robbiano, María
Martín, B. San
Keywords: Spectral graph theory
Energy of graphs
Issue Date: 15-Jan-2017
Publisher: Elsevier
Abstract: The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph.
Peer review: yes
DOI: 10.1016/j.laa.2016.10.022
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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