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arXiv · 2501.05148

D-Antimagic Labelings of Oriented Star Forests

Ahmad Muchlas Abrar·Rinovia Simanjuntak
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Abstract

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.

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Ahmad Muchlas Abrar, Rinovia Simanjuntak. 2025-01-09. D-Antimagic Labelings of Oriented Star Forests. https://arxiv.org/abs/2501.05148

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