Szczegóły publikacji
Opis bibliograficzny
Zero-sum partitions of Abelian groups and their applications to magic- and antimagic-type labelings / Sylwia CICHACZ, Karol SUCHAN // Discrete Mathematics and Theoretical Computer Science ; ISSN 1462-7264. — 2024 — vol. 26 iss. 3 art. no. 14, s. 1–27. — Bibliogr. s. 18–20, Abstr. — Publikacja dostępna online od: 2024-10-25. — K. Suchan – dod. afiliacja: Universidad Diego Portales, Santiago, Chile
Autorzy (2)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 158074 |
|---|---|
| Data dodania do BaDAP | 2025-02-19 |
| Tekst źródłowy | URL |
| DOI | 10.46298/dmtcs.12361 |
| Rok publikacji | 2024 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Discrete Mathematics and Theoretical Computer Science |
Abstract
The following problem has been known since the 80s. Let Γ be an Abelian group of order m (denoted |Γ| = m), and let t and (Formula presented), be positive integers such that (Formula presented). Determine when Γ∗ = Γ \ {0}, the set of non-zero elements of Γ, can be partitioned into disjoint subsets (Formula presented) such that |Si| = mi and (Formula presented) for every 1 ≤ i ≤ t. Such a subset partition is called a zero-sum partition. |I(Γ)| ̸= 1, where I(Γ) is the set of involutions in Γ, is a necessary condition for the existence of zero-sum partitions. In this paper, we show that the additional condition of mi ≥ 4 for every 1 ≤ i ≤ t, is sufficient. Moreover, we present some applications of zero-sum partitions to magic- and antimagic-type labelings of graphs.
