Kamatchi–Arumugam characterization conjecture for distance-antimagic graphs

Let $G$ be a graph, and let $N(u)$ denote the open neighborhood of a vertex $u$. A graph is distance antimagic if it admits a bijection $f:V(G)\to\{1,2,\ldots,|V(G)|\}$ such that the vertex weights

$$w(v)=\sum_{u\in N(v)}f(u)$$

are distinct for all vertices $v$.

Kamatchi–Arumugam conjecture. $G$ is distance antimagic if and only if $N(u)\ne N(v)$ for any two distinct vertices $u,v\in V(G)$.

The source says that this conjecture was put forward by Kamatchi and Arumugam and was still open at the time of the paper. It proposes a neighborhood-based characterization of distance-antimagic graphs.