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.