Graph energy change due to edge deletion Original Research Article

The energy of a graph is the sum of the singular values of its adjacency matrix. We are interested in how the energy of a graph changes when edges are deleted. Examples show that all cases are possible: increased, decreased, unchanged. Our goal is to find possible graph theoretical descriptions and to provide an infinite family of graphs for each case. The main tool is a singular value inequality for complementary submatrices and its equality case.