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

Day, Jane; So, Wasin

Electron. J. Linear Algebra 16, 291-299 (2007).

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.)

Keywords:

singular value inequality; graph energy; adjacency matrix