Applications of a theorem by Ky Fan in the theory of graph energy

被引：52

作者：

So, Wasin ^{[2
]}

Robbiano, Maria ^{[3
]}

Maia de Abreu, Nair Maria ^{[4
]}

Gutman, Ivan ^{[1
]}

机构：

[1] Univ Kragujevac, Fac Sci, Kragujevac 34000, Serbia

[2] San Jose State Univ, Dept Math, San Jose, CA 95192 USA

[3] Univ Catolica Norte, Antofagasta, Chile

[4] Univ Fed Rio de Janeiro, Rio De Janeiro, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 09期

关键词：

Graph spectrum; Energy (of graph); Singular value (of matrix); Ky Fan theorem; LAPLACIAN ENERGY; SPECTRUM;

D O I：

10.1016/j.laa.2009.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G, which in turn is equal to the sum of the singular values of the adjacency matrix of G. Let X, Y, and Z be matrices, such that X + Y = Z. The Ky Fan theorem establishes an inequality between the sum of the singular values of Z and the sum of the sum of the singular values of X and Y. This theorem is applied in the theory of graph energy, resulting in several new inequalities, as well as new proofs of some earlier known inequalities. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2163 / 2169

页数：7

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