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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1249,
author = {Martin Sonntag},
title = {Difference labelling of digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {24},
year = {2004},
pages = {509-527},
zbl = {1061.05083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1249}
}
Martin Sonntag. Difference labelling of digraphs. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 509-527. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1249/
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