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In this paper, we describe primary decomposition of the edge ideal of thejoin of some graphs in terms of that information of the edge ideal of everyweighted oriented graph. Meanwhile, we also study depth and regularity ofsymbolic powers and ordinary powers of such an edge ideal. We explicitlycompute depth and regularity of ordinary powers of the edge ideal of the joinof two graphs consisting of isolated vertices, and also provide upper bounds ofregularity of symbolic powers of such an edge ideal. For the edge ideal of thejoin of two graphs with at least an oriented edge for per graph, we give theexact formulas for their depth and regularity, and also provide the upperbounds of regularity of ordinary powers of such an edge ideal. Some examplesshow that these upper bounds can be obtained, but may be strict.

The edge ideals of the join of some vertex weighted oriented graphs