# Difference labelling of cacti

Discussiones Mathematicae Graph Theory (2003)

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

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topMartin 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 -

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