Geodesic
Difference labelling of digraphs
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 509-527

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A digraph G is a difference digraph iff there exists an S ⊂ N⁺ 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 source-join (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.
Keywords: graph labelling, difference digraph, oriented tree 
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     author = {Sonntag, Martin},
     title = {Difference labelling of digraphs},
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Sonntag, Martin. Difference labelling of digraphs. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 509-527. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a13/