Some properties of superline digraphs

For a given digraph G = (V, E) and a positive integer k, the super line digraph of index k of G is the digraph S_k{G) which has for vertices all the k-subsets of E(G), and two vertices S and T are adjacent whenever there exist edges in the form (u, v) isin S and (u, w) isin T for some u, v, w isin V. The super line digraph is a generalization of the super line graph. Indeed, if the digraph G is symmetric, the super line digraph of G is isomorphic to the super line graph of the graph obtained by removing the orientation of the edges of G. We study the link between properties of super line digraphs and super line graphs