Consider an order n abelian group G and a tree T on n vertices. When is it possible to (bijectively) label V(T) by G do that along all edges xy, the sums x+y are distinct? There are various motivations for studying this question, such as the Harmonious Labelling Conjecture of Graham-Sloane, which asks something related for cyclic G. This talk will be about giving a necessary and sufficient condition for the labelling to be possible in the case of arbitrary G and large, bounded degree T.
Joint work with Alp Müyesser.