The energy of C4-free graphs of bounded degree

Abstract

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, has energy greater that its order. Here, the energy of a graph is the sum of the moduli of its eigenvalues. We give more general theorems and state two conjectures.