On the spectral radius and the energy of a digraph

The energy of a digraph D is defined as E (D) = Sigma(n)(i=1) vertical bar Re (z(i))vertical bar, where z(1), ... , z(n) are the (possibly complex) eigenvalues of D. In this paper, we obtain an improved lower bound on the spectral radius of D. Considering this result, we present an upper bound on the energy of D. We also show that our results generalize and improve some known results for graphs and digraphs.