# SINGULAR VALUE INEQUALITY AND GRAPH ENERGY CHANGE

@article{Day2007SINGULARVI, title={SINGULAR VALUE INEQUALITY AND GRAPH ENERGY CHANGE}, author={J. M. Day and Wasin So}, journal={Electronic Journal of Linear Algebra}, year={2007}, volume={16}, pages={25} }

The energy of a graph is the sum of the singular values of its adjacency matrix. A classic inequality for singular values of a matrixsum, 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 matrixis nonsingular. 1. Singular value inequality for…

## 54 Citations

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The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues to their average, which in turn is equal to the sum of singular values of a shift of Laplacian matrix…

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