5-regular oriented graphs with optimum skew energy

Let G be a simple undirected graph and G^σ be the corresponding oriented graph of G with the orientation σ. The skew energy of G^σ, denoted by ε_s(G^σ), is defined as the sum of the singular values of the skew adjacency matrix S(G^σ). In 2010, Adiga et al. certified that ɛ_s(G^σ)≤nΔ, where Δ is the maximum degree of G of order n. It has been shown that every 5-regular oriented graph with optimum skew energy has even neighborhood property, that is each pair of neighborhoods of a graph have even number of common vertices. In this paper, we characterize all connected 5-regular graphs of order n with this property. Moreover, we determine all connected 5-regular oriented graphs of order n with maximum skew-energy.