Orientable -distance magic regular graphs
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 be an Abelian group of order . A directed -distance magic labeling of an oriented grap...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2021-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.06.005 |
| Summary: | 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 be an Abelian group of order . A directed -distance magic labeling of an oriented graph of order is a bijection with the property that there is a magic constant such that for every In this paper we provide an infinite family of odd regular graphs possessing an orientable -distance magic labeling. Our results refer to lexicographic product of graphs. We also present a family of odd regular graphs that are not orientable -distance magic. |
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| ISSN: | 0972-8600 2543-3474 |