Kamatchi–Arumugam's distance antimagic conjecture

Let $G=(V,E)$ be an undirected simple graph. A bijection $h:V(G)\rightarrow\{1,2,\dots,|V(G)|\}$ is a distance antimagic labeling when the vertex weights

$$\omega(u)=\sum_{v\in N(u)}h(v)$$

are distinct for all vertices $u$, where $N(u)$ is the neighborhood of $u$. Kamatchi–Arumugam's conjecture. The graph $G$ is distance antimagic if and only if no two distinct vertices have identical neighborhoods. The conjecture has been computationally verified for all graphs of order at most $8$, but its general status is not established in the supplied text.