Szczegóły publikacji
Opis bibliograficzny
A magic rectangle set on Abelian groups and its application / Sylwia CICHACZ, Tomasz Hinc // Discrete Applied Mathematics ; ISSN 0166-218X. — 2021 — vol. 288, s. 201–210. — Bibliogr. s. 210, Abstr. — Publikacja dostępna online od: 2020-09-12. — S. Cichacz - dod. afiliacja: University of Primorska, Slovenia
Autorzy (2)
- AGHCichacz-Przeniosło Sylwia
- Hinc Tomasz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 130212 |
|---|---|
| Data dodania do BaDAP | 2020-10-02 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.dam.2020.08.029 |
| Rok publikacji | 2021 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Applied Mathematics |
Abstract
A Γ-magic rectangle set MRSΓ(a,b;c) of order abc is a collection of c arrays (a×b) whose entries are elements of group Γ of order abc, each appearing once, with all row sums in every rectangle equal to a constant ω∈Γ and all column sums in every rectangle equal to a constant δ∈Γ. In this paper we prove that for {a,b}≠{2α,2k+1} where α and k>0 are some natural numbers, a Γ-magic rectangle set MRSΓ(a,b;c) exists if and only if a and b are both even or |Γ| is odd or Γ has more than one involution. We proved that there does not exist a Γ-magic rectangle set MRSΓ(2,2k+1;c) for any Abelian group Γ of order (4k+2)c. Moreover we obtain sufficient and necessary conditions for existence of a Γ-magic rectangle MRSΓ(a,b)=MRSΓ(a,b;1). This work will also be potentially useful for graph theorists who work in graph labeling. We apply the main result for construction of two group magic-type labelings for some families of graphs. In particular we give necessary and sufficient conditions for tKn,n to be Γ-magic. © 2020 Elsevier B.V.
