The adjacent vertex distinguishing chromatic conjecture

Let $G$ be a simple connected graph, and let $d45e$ denote its maximum degree. An adjacent vertex distinguishing coloring (or avd-coloring) is a proper edge coloring such that, for every pair of adjacent vertices $u$ and $v$, the sets of colors on edges incident with $u$ and $v$ are different. The avd-chromatic number is the minimum number of colors in an avd-coloring of $G$.

Zhang's conjecture. If $G\neq C_5$ and $G\neq K_2$, where $C_5$ is the cycle of size $5$, then the avd-chromatic number of $G$ is at most

$$\Delta+2.$$

Here $\Delta$ is the maximum degree of $G$. The conjecture concerns the number of colors required when incident edges must be properly colored while adjacent vertices receive distinct incident color sets; the supplied source gives no evidence of a resolution.