The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitrary edge is deleted except for the order of 4.
Corrigendum to “Proof of a conjecture on distance energy change of complete multipartite graph due to edge deletion” [Linear Algebra Appl. 611 (2021) 253–259]
