Magic Labeling

A magic labeling in one graph-labeling convention assigns the integers 1, 2, ..., to the graph edges of a tree so that the sum of the labels on the graph edges incident to each graph vertex is constant. This is a vertex-magic edge labeling. It is conjectured that every tree whose graph vertices all have degree 1 or 3 has such a labeling. Other graph-labeling conventions include edge-magic total labelings, which place labels on both graph vertices and graph edges.