ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 20(2) (2000) 255-265
DOI: 10.7151/dmgt.1124


Hanns-Martin Teichert

Institute of Mathematics
Medical University of Lübeck
Wallstraß e 40, 23560 Lübeck, Germany


A hypergraph H is a sum hypergraph iff there are a finite S ⊆ IN+ and d, [`d] ∈ IN+ with 1 < d ≤ [`d] such that H is isomorphic to the hypergraph Hd,[`d] (S) = (V,E) where V = S and E = {e ⊆ S:d ≤ |e| ≤ [`d] ∧∑v ∈ e v ∈ S}. For an arbitrary hypergraph H the sum number σ = σ(H) is defined to be the minimum number of isolated vertices y1,…, yσ ∉ V such that H∪{y1,…,yσ} is a sum hypergraph.

Generalizing the graph Cn we obtain d-uniform hypergraphs where any d consecutive vertices of Cn form an edge. We determine sum numbers and investigate properties of sum labellings for this class of cycle hypergraphs.

Keywords: hypergraphs, sum number, vertex labelling.

2000 Mathematics Subject Classification: 05C65, 05C78.


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Received 7 February 2000
Revised 7 April 2000