4-regular oriented graphs with optimum skew energies

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