# 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…

## 53 Citations

### ELA ON THE ENERGY OF SINGULAR GRAPHS

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- 2013

The nullity, η(G), of a graph G is the algebraic multiplicity of the eigenvalue zero in the graph’s spectrum. If η(G) > 0, then the graph G is said to be singular. The energy of a graph, E(G), was…

### ON THE ENERGY OF SINGULAR GRAPHS

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The nullity, �(G), of a graph G is the algebraic multiplicity of the eigenvalue zero in the graph's spectrum. If �(G) > 0, then the graph G is said to be singular. The energy of a graph, E(G), was…

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To any graph we may associate a matrix which records information about its structure. The goal of spectral graph theory is to see how the eigenvalues of such a matrix representation relate to the…

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

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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 $X$, $Y$…

### Oriented bipartite graphs with minimal trace norm

- Mathematics
- 2019

Abstract The trace norm of a digraph D is the trace norm of its adjacency matrix A (i.e. the sum of the singular values of A). In particular, when G is a graph then its trace norm is the well-known…

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