Group-harmonious labellings of trees
Combinatorics Seminar
12th May 2026, 11:00 am – 12:00 pm
Fry Building, 2.04
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.
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