It is conjectured that every Tree with edges whose nodes are all trivalent or monovalent can be given a ``magic'' labeling such that the Integers 1, 2, ..., can be assigned to the edges so that the Sum of the three meeting at a node is constant.
See also Magic Constant, Magic Cube, Magic Graph, Magic Hexagon, Magic Square
Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.