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Singular value inequality and graph energy change. (English) Zbl 1146.15008

Summary: The energy of a graph is the sum of the singular values of its adjacency matrix. A classic inequality for singular values of a matrix sum, including its equality case, is used to study how the energy of a graph changes when edges are removed. One sharp bound and one bound that is never sharp, for the change in graph energy when the edges of a nonsingular induced subgraph are removed, are established. A graph is nonsingular if its adjacency matrix is nonsingular.

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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