Szczegóły publikacji
Opis bibliograficzny
On zero sum-partition of Abelian groups into three sets and group distance magic labeling / Sylwia CICHACZ // Ars Mathematica Contemporanea ; ISSN 1855-3966. — 2017 — vol. 13 no. 2, s. 417–425. — Bibliogr. s. 425, Abstr. — Publikacja dostępna online od: 2017-05-10
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 105640 |
|---|---|
| Data dodania do BaDAP | 2017-06-07 |
| Tekst źródłowy | URL |
| DOI | 10.26493/1855-3974.1054.fcd |
| Rok publikacji | 2017 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Ars Mathematica Contemporanea |
Abstract
We say that a finite Abelian group Γ has the constant-sum-partition property into t sets (CSP(t)-property) if for every partition n = r1 + r2 + … + rt of n, with ri ≥ 2 for 2 ≤ i ≤ t, there is a partition of Γ into pairwise disjoint subsets A1, A2, …, At, such that ∣Ai∣ = ri and for some ν ∈ Γ , ∑ a ∈ Aia = ν for 1 ≤ i ≤ t. For ν = g0 (where g0 is the identity element of Γ ) we say that Γ has zero-sum-partition property into t sets (ZSP(t)-property). A Γ -distance magic labeling of a graph G = (V, E) with ∣V∣ = n is a bijection ℓ from V to an Abelian group Γ of order n such that the weight w(x) = ∑ y ∈ N(x)ℓ(y) of every vertex x ∈ V is equal to the same element μ ∈ Γ , called the magic constant. A graph G is called a group distance magic graph if there exists a Γ -distance magic labeling for every Abelian group Γ of order ∣V(G)∣. In this paper we study the CSP(3)-property of Γ , and apply the results to the study of group distance magic complete tripartite graphs.
