ELA, Volume 16, pp. 291-299, September 2007, abstract.

Singular Value Inequality and Graph Energy Change

Jane Day and Wasin So

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.