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## Discussiones Mathematicae Graph Theory

2000 | 20 | 2 | 255-265
Tytuł artykułu

### Sum labellings of cycle hypergraphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A hypergraph 𝓗 is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that 𝓗 is isomorphic to the hypergraph $𝓗_{d̲,[d̅]} (S) = (V,𝓔)$ where V = S and $𝓔 = {e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_{v∈ e} v ∈ S}$. For an arbitrary hypergraph 𝓗 the sum number σ = σ(𝓗) is defined to be the minimum number of isolated vertices $y₁,..., y_σ ∉ V$ such that $𝓗 ∪ {y₁,...,y_σ}$ 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.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
255-265
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-02-07
poprawiono
2000-04-07
Twórcy
• Institute of Mathematics, Medical University of Lübeck, Wallstraße 40, 23560 Lübeck, Germany
Bibliografia
• [1] C. Berge, Hypergraphs, (North Holland, Amsterdam - New York - Oxford - Tokyo, 1989).
• [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.
• [3] F. Harary, Sum graphs and difference graphs, Congressus Numerantium 72 (1990) 101-108.
• [4] F. Harary, Sum graphs over all the integers, Discrete Math. 124 (1994) 99-105, doi: 10.1016/0012-365X(92)00054-U.
• [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
• [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.
• [7] A. Sharary, Integral sum graphs from complete graphs, cycles and wheels, Arab. Gulf J. Scient. Res. 14 (1996) 1-14.
• [8] M. Sonntag, Antimagic and supermagic vertex-labelling of hypergraphs, Techn. Univ. Bergakademie Freiberg, Preprint 99-5 (1999).
• [9] H.-M. Teichert, Classes of hypergraphs with sum number one, Discuss. Math. Graph Theory 20 (2000) 93-103, doi: 10.7151/dmgt.1109.
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Bibliografia
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