Keywords: graph energy, cycle, path
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.
Wang, Wen-Huan and So, Wasin.
"Graph energy change due to any single edge deletion",
Electronic Journal of Linear Algebra,
Volume 29, pp. 59-73.