Properties of symbolic powers of edge ideals of weighted oriented graphs

Let [Formula: see text] be a weighted oriented graph and its edge ideal. We provide one method to find all the minimal generators of text], where is maximal strong vertex cover intersections irreducible ideals associated covers contained in text]. If an induced digraph under certain condition on we show that for some implies necessary sufficient equality ordinary symbolic powers ideal union two naturally paths with common sink vertex. characterize such at most into each vertices if Finally, rooted tree degree root when