Abstract

Let D be a simple digraph with eigenvalues z 1, z 2, …, z n. The energy of D is defined as (Formula presented.), where Re(z i) is the real part of the eigenvalue z i. In this paper, a lower bound for the spectral radius of D will be established based on the number of subgraphs (Formula presented.) in D, improving some of the lower bounds that appear in the literature. Furthermore, this result allows us to obtain an upper bound for the energy of D.