Abstract

Let D be a simple digraph with eigenvalues z(1), z(2),...,z(n). The energy of D is defined as E(D) = Sigma(n)(i=n) vertical bar Re(z(i))vertical bar, 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 (P-3)over-left-right-arrow 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.