Hartsfield–Ringle antimagic labeling conjecture for connected graphs

Let $G$ be a simple connected graph, and let an antimagic labeling be a bijection from $E(G)$ to $\{1,\dotsc,|E(G)|\}$ for which the vertex sums—the sums of labels on edges incident to each vertex—are pairwise distinct. Hartsfield–Ringle's conjecture. Every simple connected graph other than $K_2$ is antimagic. This is a central conjecture in graph labeling; it is known for several graph classes and for graphs of sufficiently large minimum degree, but remains open for general connected graphs.