Orientations of 2-regular graphs admitting D-antimagic labelings

Find all orientations of a 2-regular graph that admit a D-antimagic labeling.

Background

The paper characterizes several restricted classes of D-antimagic oriented 2-regular graphs, including singleton distance sets and Θ-oriented 2-regular graphs. It does not provide a complete classification for arbitrary orientations, so the final open problem asks for all orientations that support a D-antimagic labeling.

References

We conclude by proposing the following general open problem. Find all possible orientations of a 2-regular graph admitting a $D$-antimagic labeling.

— D-Antimagic Labelings of Oriented 2-Regular Graphs  (2501.05123 - Abrar et al., 9 Jan 2025) in Section 3, final paragraph of the paper