# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

## SUM LABELLINGS OF CYCLE HYPERGRAPHS

Hanns-Martin Teichert

Institute of Mathematics
Medical University of Lübeck
Wallstraß e 40, 23560 Lübeck, Germany
e-mail: teichert@math.mu-luebeck.de

## Abstract

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.

## References

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