D-Antimagic Labelings of Oriented Star Forests
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912182044721152 |
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| author | Abrar, Ahmad Muchlas Simanjuntak, Rinovia |
| author_facet | Abrar, Ahmad Muchlas Simanjuntak, Rinovia |
| contents | For a distance set $D$, an oriented graph $\overrightarrow{G}$ is $D$-antimagic if there exists a bijective vertex labeling such that the sum of all labels of $D$-out-neighbors is distinct for each vertex. This paper provides all orientations and all possible $D$s of a $D$-antimagic oriented star. We provide necessary and sufficient condition for $D$-antimagic oriented star forest containing isomorphic oriented stars. We show that for all possible $D$s, there exists an orientation for a star forest to admit a $D$-antimagic labeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | D-Antimagic Labelings of Oriented Star Forests Abrar, Ahmad Muchlas Simanjuntak, Rinovia Combinatorics 05C78 05C78 05C78 For a distance set $D$, an oriented graph $\overrightarrow{G}$ is $D$-antimagic if there exists a bijective vertex labeling such that the sum of all labels of $D$-out-neighbors is distinct for each vertex. This paper provides all orientations and all possible $D$s of a $D$-antimagic oriented star. We provide necessary and sufficient condition for $D$-antimagic oriented star forest containing isomorphic oriented stars. We show that for all possible $D$s, there exists an orientation for a star forest to admit a $D$-antimagic labeling. |
| title | D-Antimagic Labelings of Oriented Star Forests |
| topic | Combinatorics 05C78 05C78 05C78 |
| url | https://arxiv.org/abs/2501.05148 |