Classes of hypergraphs with sum number one

• Autorzy: Hanns-Martin Teichert
• Języki publikacji: EN

Abstrakty

EN

A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ 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(ℋ ) is defined to be the minimum number of isolatedvertices $w₁,..., w_σ∉ V$ such that $ℋ ∪ {w₁,..., w_σ}$ is a sum hypergraph.
For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs 𝓒ₙ and 𝓦ₙ that under a certain condition for the edgecardinalities (𝓒ₙ)= (𝓦ₙ)=1

Słowa kluczowe

EN

hypergraphs; sum number; vertex labelling

Kategorie tematyczne

• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)
• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 93-103

Daty

wydano

2000

otrzymano

1999-05-04

poprawiono

1999-09-28

Twórcy

autor

Hanns-Martin Teichert

• 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] D. Bergstrand, F. Harary, K. Hodges, G. Jennings, L. Kuklinski and J. Wiener, The Sum Number of a Complete Graph, Bull. Malaysian Math. Soc. (Second Series) 12 (1989) 25-28.
• [3] M.N. Ellingham, Sum graphs from trees, Ars Combin. 35 (1993) 335-349.
• [4] F. Harary, Sum Graphs and Difference Graphs, Congressus Numerantium 72 (1990) 101-108.
• [5] F. Harary, Sum Graphs over all the integers, Discrete Math. 124 (1994)99-105, doi: 10.1016/0012-365X(92)00054-U.
• [6] N. Hartsfield and W.F. Smyth, The Sum Number of Complete Bipartite Graphs, in: R. Rees, ed., Graphs and Matrices (Marcel Dekker, New York, 1992) 205-211.
• [7] N. Hartsfield and W.F. Smyth, A family of sparse graphs with large sum number, Discrete Math. 141 (1995) 163-171, doi: 10.1016/0012-365X(93)E0196-B.
• [8] M. Miller, Slamin, J. Ryan, W.F. Smyth, Labelling Wheels for Minimum Sum Number, J. Comb. Math. and Comb. Comput. 28 (1998) 289-297.
• [9] M. Sonntag and H.-M. Teichert, Sum numbers of hypertrees, Discrete Math. 214 (2000) 285-290, doi: 10.1016/S0012-365X(99)00307-6.
• [10] M. Sonntag and H.-M. Teichert, On the sum number and integral sum number of hypertrees and complete hypergraphs, Proc. 3rd Krakow Conf. on Graph Theory (1997), to appear.
• [11] H.-M. Teichert, The sum number of d-partite complete hypergraphs, Discuss. Math. Graph Theory 19 (1999) 79-91, doi: 10.7151/dmgt.1087.

Identyfikatory

DOI

10.7151/dmgt.1109