A Survey of Graceful Trees
نویسندگان
چکیده
A tree of order n is said to be graceful if the vertices can be assigned the labels {0, . . . , n−1} such that the absolute value of the differences in vertex labels between adjacent vertices generate the set {1, . . . , n− 1}. The Graceful Tree Conjecture is the unproven claim that all trees are graceful. We present major results known on graceful trees from those dating from the problem’s origin to recent developments. Constructions and classes of graceful trees are given as well as an analysis of various lines of attack on the Conjecture. We also examine other types of graph labellings as they relate to the Conjecture.
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