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arXiv · 2501.05123

D-Antimagic Labelings of Oriented 2-Regular Graphs

Ahmad Muchlas Abrar·Rinovia Simanjuntak
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Abstract

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 $\Theta$-oriented cycles. Finally, we characterize $D$-antimagic oriented 2-regular graphs, when $|D|=1$, and $D$-antimagic $\Theta$-oriented 2-regular graphs.

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Ahmad Muchlas Abrar, Rinovia Simanjuntak. 2025-01-09. D-Antimagic Labelings of Oriented 2-Regular Graphs. https://arxiv.org/abs/2501.05123

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