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Discussiones Mathematicae Graph Theory 24(3) (2004) 509-527
DOI: https://doi.org/10.7151/dmgt.1249

DIFFERENCE LABELLING OF DIGRAPHS

Martin Sonntag

Faculty of Mathematics and Computer Science
TU Bergakademie Freiberg
Agricola-Str. 1, D-09596 Freiberg, Germany
e-mail: [email protected]

Abstract

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.

2000 Mathematics Subject Classification: 05C78, 05C20.

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Received 21 July 2003
Revised 24 February 2004