Singular value inequality and graph energy change

Abstract

The energy of a graph is the sum of the singular values of its adjacency matrix. Aclassic inequality for singular values of a matrixsum, including its equality case, is used to studyhow the energy of a graph changes when edges are removed. One sharp bound and one bound thatis never sharp, for the change in graph energy when the edges of a nonsingular induced subgraph areremoved, are established. A graph is nonsingular if its adjacency matrixis nonsingular.