Graphs admitting antimagic labeling for arbitrary sets of positive numbers

Hartsfield and Ringel in 1990 conjectured that any connected graph with q≥2 edges has an edge labeling f with labels in the set {1,…,q}, such that for every two distinct vertices u and v, fu≠fv, where fv=∑e∈E(v)f(e), and E(v) is the set of edges of the graph incident to vertex v.