Liu–Wang–Zhang's conjecture on the neighbourhood distinguishing index

Let $G$ be a connected graph, let $\Delta(G)$ be its maximum degree, and let $\operatorname{ndi}(G)$ be the smallest number of colours in a proper edge colouring for which adjacent vertices receive distinct sets of colours on their incident edges.

Liu–Wang–Zhang's conjecture. If $G\notin\{K_2,C_5\}$, then

$$\Delta(G)\leq \operatorname{ndi}(G)\leq \Delta(G)+2.$$

The lower bound is immediate, while the upper bound is known for bipartite graphs and graphs with maximum degree at most three, but remains open in general.