Energy of Graphs with Self-Loops

Abstract

The energy of graphs containing self-loops is considered. If the graph G of order n contains σ self-loops, then its energy is defined as E(G) = P |λi − σ/n| where λ1, λ2, . . ., λn 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.