# Difference labelling of digraphs

• Volume: 24, Issue: 3, page 509-527
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Martin Sonntag. "Difference labelling of digraphs." Discussiones Mathematicae Graph Theory 24.3 (2004): 509-527. <http://eudml.org/doc/270712>.

@article{MartinSonntag2004,
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.},
author = {Martin Sonntag},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph labelling; difference digraph; oriented tree; graph labeling},
language = {eng},
number = {3},
pages = {509-527},
title = {Difference labelling of digraphs},
url = {http://eudml.org/doc/270712},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Martin Sonntag
TI - Difference labelling of digraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 3
SP - 509
EP - 527
AB - 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.
LA - eng
KW - graph labelling; difference digraph; oriented tree; graph labeling
UR - http://eudml.org/doc/270712
ER -

## References

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