Lower bounds of Nikiforov's energy over digraphs

The energy of a graph G is defined as E(G) = Sigma(n)(i=1) vertical bar lambda(i)vertical bar, where lambda(1), lambda(2), ..., lambda(n) are the eigenvalues of the adjacency matrix of G. This concept was extended by Nikiforov [8] to digraphs as N (D) Sigma(n)(i=1) sigma(i), where D is a digraph with n vertices and singular values sigma(1), ..., sigma(n). Upper bounds of N were found by Kharaghani and Tayfeh-Rezaie [4]. In this work we find lower bounds of N over the set of digraphs. (C) 2016 Elsevier Inc. All rights reserved.