Some Sharp Bounds for the Spectral Radius and Energy of Digraphs

Abstract

For a simple digraph \(D\) with \(n\) vertices, the energy of \(D\) is defined as \(E(D) = \sum_{i=1}^{n} |\Re(z_i)|\), where \(z_1, z_2, \ldots, z_n\) are the eigenvalues of \(D\). This paper first gives an improved lower bound on the spectral radius of \(D\), which is used to obtain some upper bounds for the energy \(E(D)\). These results improve and generalize some known results on upper bounds of the energy of digraphs.