Lower bounds of Nikiforov's energy over digraphs

The energy of a graph G is defined as E(G)=∑i=1n|λi|, where λ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G. This concept was extended by Nikiforov [8] to digraphs as N(D)=∑i=1nσi, where D is a digraph with n vertices and singular values σ1,…,σn. 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.