The super edge-magic odd constellation conjecture

Let a constellation be a forest whose components are stars, and call it odd when it consists of an odd number of stars. A labeling of a graph is super edge-magic if it is an edge-magic labeling whose vertex labels are exactly the smallest possible vertex-label set. Lee--Kong's conjecture. Every odd constellation is super edge-magic. This conjecture concerns super edge-magic labelings of forests formed from stars and was posed in 2002; the paper investigates this problem along with related forests of caterpillars.