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Applications of a theorem by Ky Fan in the theory of graph energy |
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| Authors: | Wasin So |
| Affiliation: | a Department of Mathematics, San Jose State University, San Jose, CA 95192-0103, USA b Universidad Católica del Norte, Antofagasta, Chile c Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil d Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia |
| Abstract: | 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. |
| Keywords: | 05C50 05C90 |
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