| Autor: |
Dyrlaga, Paweł, Szopa, Karolina |
| Zdroj: |
AKCE International Journal of Graphs and Combinatorics; 20240101, Issue: Preprints |
| Abstrakt: |
Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation (Hefetz et al., 2010). In this paper we support the analogous question for distance magic labeling. Let Γbe an Abelian group of order n. A directedΓ-distance magic labelingof an oriented graph G→=(V,A)of order nis a bijection l→:V→Γwith the property that there is a magic constantμ∈Γsuch that for every x∈V(G)w(x)=∑y∈N+(x)l→(y)−∑y∈N−(x)l→(y)=μ.In this paper we provide an infinite family of odd regular graphs possessing an orientable Zn-distance magic labeling. Our results refer to lexicographic product of graphs. We also present a family of odd regular graphs that are not orientable Zn-distance magic. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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