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of such that if denotes the sum of the labels on the neighbors of , then is a vertex coloring of . The "lucky number" of is the least such that has a lucky labeling with the integers

Antimagic labeling

An antimagic labeling of a graph is a one-to-one assignment of the positive integers } to the edges of such that all induced vertex weights are distinct, where the weight of a vertex is the sum of the labels on all edges incident to it.

Magic labeling

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