Bounds for the energy of normal digrahs

摘要

The low energy of a digraph D with eigenvalues z _1,...,z _n is defined as e(D)=∑ ~n _(i=1){pipe}Re(z ~i){pipe}, where Re(z _i) is the real part of the complex number z i. The main results in this article generalize Koolen-Moulton upper bounds for the energy of graphs to normal digraphs, i.e. digraphs with normal adjacency matrix. We show that this new bound improves the generalized McClelland upper bound for the low energy of a digraph. Also, we give a sharp lower bound for the low energy of normal digraphs.