The energy of C4-free graphs of bounded degree Original Research Article

Answering some questions of Gutman, we show that, except for four specific trees, every connected graph G of order n, with no cycle of order 4 and with maximum degree at most 3, satisfiesmidμ1mid+cdots, three dots, centered+midμnmidgreater-or-equal, slantedn,where μ1,…,μn are the eigenvalues of G. We give some general results and state two conjectures.