Abstract
The energy of graphs containing self-loops is considered. If the graph \(G\) of order \(n\) contains \(\sigma\) self-loops, then its energy is defined as \(E(G) = \sum |\lambda_i − \sigma/n|\) where \(\lambda_1, \lambda_2,\dots, \lambda_n\) are the eigenvalues of the adjacency matrix of \(G\). Some basic properties of \(E(G)\) are established, and several open problems pointed out or conjectured.