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.
Magic Labeling
See also
Magic Constant, Magic Cube, Magic Graph, Magic Hexagon, Magic SquareExplore with Wolfram|Alpha
References
Guy, R. K. "Unsolved Problems Come of Age." Amer. Math. Monthly 96, 903-909, 1989.Referenced on Wolfram|Alpha
Magic LabelingCite this as:
Weisstein, Eric W. "Magic Labeling." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicLabeling.html