  Let $G$ be a simple undirected graph, and $G^\sigma$ be an oriented graph of
$G$ with the orientation $\sigma$ and skew-adjacency matrix $S(G^\sigma)$. The
skew energy of the oriented graph $G^\sigma$, denoted by
$\mathcal{E}_S(G^\sigma)$, is defined as the sum of the absolute values of all
the eigenvalues of $S(G^\sigma)$. In this paper, we characterize the underlying
graphs of all 4-regular oriented graphs with optimum skew energy and give
orientations of these underlying graphs such that the skew energy of the
resultant oriented graphs indeed attain optimum. It should be pointed out that
there are infinitely many 4-regular connected optimum skew energy oriented
graphs, while the 3-regular case only has two graphs: $K_4$ the complete graph
on 4 vertices and $Q_3$ the hypercube.
