A lower bound for the energy of symmetric matrices and graphs
A lower bound for the energy of symmetric matrices and graphs
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DOI：
10.1016/j.laa.2016.10.022
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发表时间：
2017-01
影响因子：
1.1
通讯作者：
Enide Andrade;María Robbiano;B. S. Martin
中科院分区：
文献类型：
--
作者：
Enide Andrade;María Robbiano;B. S. Martin
对称矩阵的能量是其特征值的绝对值之和。我们给出了分块对称矩阵的能量下界。这个界与它的商阵的谱有关。此外，我们还研究了平等的必要条件。给出了任意图的广义合成的能量的应用。给出了有桥的图的能量的一个下界。一些计算实验表明，在某些情况下，所得到的下界与众所周知的下界2m是不可比的，其中m是图的边数。
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 matrix partitioned 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 m, where m is the number of edges of the graph.