Difference labelling of digraphs

A digraph G is a difference digraph iff there exists an S ⊂ IN such that G is isomorphic to the digraph DD(S) = (V,A), where V = S and A = {(i, j) : i, j ∈ V ∧ i− j ∈ V }. For some classes of digraphs, e.g. alternating trees, oriented cycles, tournaments etc., it is known, under which conditions these digraphs are difference digraphs (cf. [5]). We generalize the so-called sourcejoin (a construction principle to obtain a new difference digraph from two given ones (cf. [5])) and construct a difference labelling for the source-join of an even number of difference digraphs. As an application we obtain a sufficient condition guaranteeing that certain (non-alternating) trees are difference digraphs.