Szczegóły publikacji
Opis bibliograficzny
Group distance magic and antimagic hypercubes / M. Anholcer, S. CICHACZ, D. Froncek, R. Simanjuntak, J. Qiu // Discrete Mathematics ; ISSN 0012-365X. — 2021 — vol. 344 iss. 12 art. no. 112625, s. 1–10. — Bibliogr. s. 10, Abstr. — Publikacja dostępna online od: 2021-09-16
Autorzy (5)
- Anholcer Marcin
- AGHCichacz-Przeniosło Sylwia
- Froncek Dalibor
- Simanjuntak R.
- Qiu J.
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 136416 |
|---|---|
| Data dodania do BaDAP | 2021-09-28 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.disc.2021.112625 |
| Rok publikacji | 2021 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Mathematics |
Abstract
Let G = (V , E) be a graph. A distance magic labeling of G is a bijective assignment of labels from {1, 2,...,|V (G)|} to the vertices of G such that the sum of labels on neighbors of u is the same for all vertices u. It is known that the n-dimensional hypercube Qn has a distance magic labeling if and only if n ≡ 2 (mod 4). Let be an Abelian group of order |V (G)|. Analogously, a -distance magic labeling of G is a bijection : V → for which the sum of labels on neighbors of u is the same for all vertices u. In this paper we fully characterize -distance magic labellings of n-dimensional hypercubes Qn. Namely we prove that for n odd, there does not exist a -distance magic labeling of Qn for any Abelian group of order |V (Qn)|, whereas for n even there exists a -distance magic labeling of Qn for every Abelian group of order |V (Qn)|. Similarly distance antimagic and -distance antimagic labellings can be defined, where one aims to find a bijection such that the sums of labels are pairwise distinct for all the vertices. We study this problem and show in particular that there exists a -distance antimagic labeling of Qn for any Abelian group of order 2n if n is odd. We also indicate some relationships between -closed distance magic and antimagic labellings and -distance antimagic labellings. The proofs rely mostly on linear algebra.
