The neighborhood characterization conjecture for distance antimagic graphs

Let $G$ be a graph. A $D$-neighborhood of a vertex is the set of vertices at distance at most $D$ from it. Neighborhood characterization conjecture. A graph is $D$-distance antimagic if and only if it does not contain two vertices with the same $D$-neighborhood.

This conjecture proposes that the necessary condition established earlier in the paper is also sufficient. The source indicates that proving or disproving it is likely to be a hard problem.