Langford sequences and a product of digraphs

Skolem and Langford sequences and their many generalizations have applications in numerous areas. The ${\otimes }_h$-product is a generalization of the direct product of digraphs. In this paper we use the ${\otimes }_h$-product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.