Optimum skew energy of a tournament

Let G be a simple undirected graph and Gσ the corresponding oriented graph of G with the orientation σ. The skew energy of Gσ, denoted by ε(Gσ), is defined as the sum of the singular values of its skew adjacency matrix S(Gσ). In 2010, Adiga et al. proved ε(Gσ)≤nΔ, where Δ is the maximum degree of G of order n. In this paper, we characterize the skew energy of a tournament and present some properties about an optimum skew energy tournament.