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 1, . . . , m 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 paper we discuss antimagic properties of graphs which contain vertices of large degree. We also show that graphs with maximum degree at least n−3 are antimagic.