On upper bounds for the energy of digraphs

The energy of a digraph D is defined as , where z1,z2,…,zn are the (possibly complex) eigenvalues of D. In this paper, we first give an improved lower bound on the spectral radius of the digraph D. Using this result, we obtain a new upper bound on the energy E(D) and characterize some extreme digraphs which attain this upper bound. This result theoretically improves and generalizes some known results.