4-regular oriented graphs with optimum skew energies

The skew energy of an oriented graph GσGσ, denoted by Es(Gσ)Es(Gσ), is defined as the sum of the singular values of its skew adjacency matrix S(Gσ)S(Gσ). The connected kk-regular oriented graph on nn vertices having skew energy kn is called the optimum skew energy kk-regular oriented graph. In this paper, we determine the 4-regular graphs GG such that each of them has an orientation σσ satisfying GσGσ which is an optimum skew energy oriented graph. In addition, as by-product we obtain a method to construct optimum skew energy kk-regular oriented graphs with large order.