D-Antimagic Labelings of Oriented 2-Regular Graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929668129554432 |
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| author | Abrar, Ahmad Muchlas Simanjuntak, Rinovia |
| author_facet | Abrar, Ahmad Muchlas Simanjuntak, Rinovia |
| contents | Given an oriented graph $\overrightarrow{G}$ and $D$ a distance set of $\overrightarrow{G}$, $\overrightarrow{G}$ is $D$-antimagic if there exists a bijective vertex labeling such that the sum of all labels of the $D$-out-neighbors of each vertex is distinct.
This paper investigates $D$-antimagic labelings of 2-regular oriented graphs. We characterize $D$-antimagic oriented cycles, when $|D|=1$; $D$-antimagic unidirectional odd cycles, when $|D|=2$; and $D$-antimagic $Θ$-oriented cycles. Finally, we characterize $D$-antimagic oriented 2-regular graphs, when $|D|=1$, and $D$-antimagic $Θ$-oriented 2-regular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05123 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | D-Antimagic Labelings of Oriented 2-Regular Graphs Abrar, Ahmad Muchlas Simanjuntak, Rinovia Combinatorics 05C78 Given an oriented graph $\overrightarrow{G}$ and $D$ a distance set of $\overrightarrow{G}$, $\overrightarrow{G}$ is $D$-antimagic if there exists a bijective vertex labeling such that the sum of all labels of the $D$-out-neighbors of each vertex is distinct. This paper investigates $D$-antimagic labelings of 2-regular oriented graphs. We characterize $D$-antimagic oriented cycles, when $|D|=1$; $D$-antimagic unidirectional odd cycles, when $|D|=2$; and $D$-antimagic $Θ$-oriented cycles. Finally, we characterize $D$-antimagic oriented 2-regular graphs, when $|D|=1$, and $D$-antimagic $Θ$-oriented 2-regular graphs. |
| title | D-Antimagic Labelings of Oriented 2-Regular Graphs |
| topic | Combinatorics 05C78 |
| url | https://arxiv.org/abs/2501.05123 |