Hartsfield's antimagic conjecture for connected graphs

Let $G$ be a connected graph. An antimagic labeling of $G$ is a bijection $f:E(G)\to\{1,\ldots,|E(G)|\}$ such that the vertex weights

$$w(v)=\sum_{e\in E(v)}f(e)$$

are distinct for every pair of distinct vertices $u,v\in V(G)$. Hartsfield's antimagic conjecture. Every connected graph other than $K_2$ is antimagic, meaning that it admits an antimagic labeling. This is one of the principal open conjectures on antimagic graph labelings and would establish the existence of such a labeling for every connected graph except the single edge.