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 and , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1185,
author = {Martin Sonntag},
title = {Difference labelling of cacti},
journal = {Discussiones Mathematicae Graph Theory},
volume = {23},
year = {2003},
pages = {55-65},
zbl = {1054.05090},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1185}
}
Martin Sonntag. Difference labelling of cacti. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 55-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1185/
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