# Sum labellings of cycle hypergraphs

• Volume: 20, Issue: 2, page 255-265
• ISSN: 2083-5892

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## Abstract

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A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph ${}_{d̲,\left[d̅\right]}\left(S\right)=\left(V,\right)$ where V = S and $=e\subseteq S:d̲\le |e|\le \left[d̅\right]\wedge {\sum }_{v\in e}v\in S$. For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices $y₁,...,{y}_{\sigma }\notin V$ such that $\cup y₁,...,{y}_{\sigma }$ 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.

## How to cite

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Hanns-Martin Teichert. "Sum labellings of cycle hypergraphs." Discussiones Mathematicae Graph Theory 20.2 (2000): 255-265. <http://eudml.org/doc/270630>.

@article{Hanns2000,
abstract = {A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph $_\{d̲,[d̅]\} (S) = (V,)$ where V = S and $= \{e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_\{v∈ e\} v ∈ S\}$. For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices $y₁,..., y_σ ∉ V$ such that $∪ \{y₁,...,y_σ\}$ 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.},
author = {Hanns-Martin Teichert},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hypergraphs; sum number; vertex labelling; sum hypergraph; sum labellings},
language = {eng},
number = {2},
pages = {255-265},
title = {Sum labellings of cycle hypergraphs},
url = {http://eudml.org/doc/270630},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Hanns-Martin Teichert
TI - Sum labellings of cycle hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2000
VL - 20
IS - 2
SP - 255
EP - 265
AB - A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph $_{d̲,[d̅]} (S) = (V,)$ where V = S and $= {e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_{v∈ e} v ∈ S}$. For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices $y₁,..., y_σ ∉ V$ such that $∪ {y₁,...,y_σ}$ 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.
LA - eng
KW - hypergraphs; sum number; vertex labelling; sum hypergraph; sum labellings
UR - http://eudml.org/doc/270630
ER -

## References

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6. [6] M. Miller, J.F. Ryan and W.F. Smyth, The Sum Number of the cocktail party graph, Bull. of the ICA 22 (1998) 79-90. Zbl0894.05048
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