Sum labellings of cycle hypergraphs

Hanns-Martin Teichert

Discussiones Mathematicae Graph Theory (2000)

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

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 d ̲ , [ d ̅ ] ( S ) = ( V , ) where V = S and = e ⊆ S : d ̲ ≤ | e | ≤ [ d ̅ ] ∧ ∑ v ∈ e v ∈ S . For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices y ₁ , . . . , y σ ∉ V such that ∪ y ₁ , . . . , 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.

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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  2. [2] J.C. Bermond, A. Germa, M.C. Heydemann and D. Sotteau, Hypergraphes hamiltoniens, Probl. Comb. et Théorie des Graphes, Orsay 1976, Colloques int. CNRS 260 (1978) 39-43. 
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  5. [5] G.Y. Katona and H.A. Kierstead, Hamiltonian chains in hypergraphs, J. Graph Theory 30 (1999) 205-212, doi: 10.1002/(SICI)1097-0118(199903)30:3<205::AID-JGT5>3.0.CO;2-O Zbl0924.05050
  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
  7. [7] A. Sharary, Integral sum graphs from complete graphs, cycles and wheels, Arab. Gulf J. Scient. Res. 14 (1996) 1-14. Zbl0856.05088
  8. [8] M. Sonntag, Antimagic and supermagic vertex-labelling of hypergraphs, Techn. Univ. Bergakademie Freiberg, Preprint 99-5 (1999). 
  9. [9] H.-M. Teichert, Classes of hypergraphs with sum number one, Discuss. Math. Graph Theory 20 (2000) 93-103, doi: 10.7151/dmgt.1109. Zbl0959.05078

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