Repositório Institucional da Universidade de Aveiro > CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações > CIDMA - Artigos > A lower bound for the energy of symmetric matrices and graphs
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 title: A lower bound for the energy of symmetric matrices and graphs authors: Andrade, EnideRobbiano, MaríaMartín, B. San keywords: Spectral graph theoryEnergy 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. URI: http://hdl.handle.net/10773/16240 ISSN: 0024-3795 publisher version/DOI: http://dx.doi.org/10.1016/j.laa.2016.10.022 source: Linear Algebra and its Applications appears in collections CIDMA - Artigos

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