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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
References
Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.