Cichacz–Froncek conjecture on distance magic graphs

Let $G$ be a graph. A distance magic labeling of $G$ is a bijection from its vertices to the cyclic group of order $|V(G)|$ for which every vertex has the same neighbor-sum. A graph is group distance magic if it admits a $\Gamma$-distance magic labeling for every Abelian group $\Gamma$ of order $|V(G)|$.

Cichacz–Froncek conjecture. If $G$ is a distance magic graph, then $G$ is group distance magic.

The conjecture asks whether existence of a distance magic labeling with the cyclic group always implies existence of such a labeling for every Abelian group of the same order. The source presents this as an open conjecture and notes that many distance magic graphs are already known to be group distance magic.