Abstract
The energy \(\mathcal{E}(G)\) of a graph \(G\) is the sum of the absolute values of all eigenvalues of \(G\). An interesting and "hard-to-crack" problem about graph energy was mentioned by Gutman in [The energy of a graph: old and new results]: characterize the graphs \(G\) and their edges \(e\) for which \(\mathcal{E}(G-e)<\mathcal{E}(G)\). In this paper, we give a new sufficient condition for \(\mathcal{E}(G-e)<\mathcal{E}(G)\) where \(e\) is not necessarily to be a cut-edge set or a cut edge. This work can be used to generalize some well-known results.
