Skew Randic matrix and skew Randic energy

‎Let $G$ be a simple graph with an orientation $sigma$‎, ‎which‎ ‎assigns to each edge a direction so that $G^sigma$ becomes a‎ ‎directed graph‎. ‎$G$ is said to be the underlying graph of the‎ ‎directed graph $G^sigma$‎. ‎In this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with Randic weight‎, ‎the skew Randic matrix ${bf‎ ‎R_S}(G^sigma)$‎, ‎of $G^sigma$ as the real skew symmetric matrix‎ ‎$[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{frac{1}{2}}$ and‎ ‎$(r_s)_{ji} =‎ ‎(d_id_j)^{frac{1}{2}}$ if $v_i rightarrow v_j$ is‎ ‎an arc of $G^sigma$‎, ‎otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$‎. ‎We‎ ‎derive some properties of the skew Randic energy of an oriented‎ ‎graph‎. ‎Most properties are similar to those for the skew energy of‎ ‎oriented graphs‎. ‎But‎, ‎surprisingly‎, ‎the extremal oriented graphs‎ ‎with maximum or minimum skew Randic energy are completely‎ ‎different‎, ‎no longer being some kinds of oriented regular graphs‎.