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Discussiones
Mathematicae Graph Theory 23(1) (2003)
55-65
DOI: https://doi.org/10.7151/dmgt.1185
DIFFERENCE LABELLING OF CACTI
Martin Sonntag
Faculty of Mathematics and Computer Science
TU Bergakademie Freiberg
Agricola-Str. 1
D-09596 Freiberg, Germany
e-mail: M.Sonntag@math.tu-freiberg.de
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 Kn,n and Kn,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.
Keywords: graph labelling, difference graph, cactus.
2000 Mathematics Subject Classification: 05C78.
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Revised 20 May 2002
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