Edge addition, singular values, and energy of graphs and matrices
Edge addition, singular values, and energy of graphs and matrices
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DOI：
10.1016/j.laa.2008.11.027
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发表时间：
2009-04
影响因子：
1.1
通讯作者：
S. Akbari;E. Ghorbani;M. Oboudi
中科院分区：
文献类型：
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作者：
S. Akbari;E. Ghorbani;M. Oboudi
一个图/矩阵的能量是它的特征值的绝对值之和。我们研究了复制/移除一条边对图能量的影响。我们还处理了一个问题，哪些图G具有这样的性质如果G的边被一些子图覆盖，那么G的能量不超过子图能量的总和。这个问题是在矩阵能量的一般设置下解决的，这也导致我们考虑奇异值。在其他结果中表明，当增加一条新边或删除一条旧边时，完全多部图的能量增加。
The energy of a graph/matrix is the sum of the absolute values of its eigenvalues. We investigate the result of duplicating/removing an edge to the energy of a graph. We also deal with the problem that which graphs G have the property that if the edges of G are covered by some subgraphs, then the energy of G does not exceed the sum of the subgraphs’ energies. The problems are addressed in the general setting of energy of matrices which leads us to consider the singular values too. Among the other results it is shown that the energy of a complete multipartite graph increases if a new edge added or an old edge is deleted.