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Antimagic Properties of Graphs with Large Maximum Degree



An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges to the integers math formula such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called antimagic if it has an antimagic labeling. In this article, we discuss antimagic properties of graphs that contain vertices of large degree. We also show that graphs with maximum degree at least math formula are antimagic.