Antimagic graph — антимагический граф.
An antimagic graph is a graph whose edges can be labeled with integers so that the sum of the labels at any given vertex is different from the sum of the labels of any other vertex, that is, no two vertices have the same sum. Hartsfield and Ringel conjecture that every tree other than is antimagic and, more strongly, that every connected graph other than is antimagic.
A special case is an -antimagic graph. The weight of a vertex under an edge labeling is the sum of values assigned to all edges incident with a given vertex . A connected graph is said to be -antimagic if there exist positive integers and a bijection such that the induced mapping is also bijection, where is the set of the weights of vertices.