On the energy of digraphs

Abstract

Let $D$ be a simple digraph with eigenvalues $z_1,z_2,...,z_n$. The energy of $D$ is defined as $E(D)= \sum_{i=1}^n |Re(z_i)|$, is the real part of the eigenvalue $z_i$. In this paper a lower bound will be obtained for the spectral radius of $D$, wich improves some the lower bounds that appear in the literature \cite{G-R}, \cite{T-C}. This result allows us to obtain an upper bound for the energy of $ D $. Finally, digraphs are characterized in which this upper bound improves the bounds given in \cite{G-R} and \cite{T-C}.