# Difference labelling of cacti

• Volume: 23, Issue: 1, page 55-65
• ISSN: 2083-5892

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## Abstract

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A graph G is a difference graph iff there exists S ⊂ IN⁺ such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = i,j:i,j ∈ V ∧ |i-j| ∈ V. It is known that trees, cycles, complete graphs, the complete bipartite graphs ${K}_{n,n}$ and ${K}_{n,n-1}$, pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a girth of at least 6 are difference graphs, too.

## How to cite

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Martin Sonntag. "Difference labelling of cacti." Discussiones Mathematicae Graph Theory 23.1 (2003): 55-65. <http://eudml.org/doc/270668>.

@article{MartinSonntag2003,
abstract = {A graph G is a difference graph iff there exists S ⊂ IN⁺ such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = i,j:i,j ∈ V ∧ |i-j| ∈ V. It is known that trees, cycles, complete graphs, the complete bipartite graphs $K_\{n,n\}$ and $K_\{n,n-1\}$, pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a girth of at least 6 are difference graphs, too.},
author = {Martin Sonntag},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph labelling; difference graph; cactus},
language = {eng},
number = {1},
pages = {55-65},
title = {Difference labelling of cacti},
url = {http://eudml.org/doc/270668},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Martin Sonntag
TI - Difference labelling of cacti
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 1
SP - 55
EP - 65
AB - A graph G is a difference graph iff there exists S ⊂ IN⁺ such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = i,j:i,j ∈ V ∧ |i-j| ∈ V. It is known that trees, cycles, complete graphs, the complete bipartite graphs $K_{n,n}$ and $K_{n,n-1}$, pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a girth of at least 6 are difference graphs, too.
LA - eng
KW - graph labelling; difference graph; cactus
UR - http://eudml.org/doc/270668
ER -

## References

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