Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers - Yi-Wu Chang; Shan-Pang Liu (Journal of Mathematics)
An edge labeling of graph G with labels in A is an injection from EG to A, where EG is the edge set of G, and A is a subset of ℝ. A graph G is called ℝ-antimagic if for each subset A of ℝ with A=EG, there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K1) and cycles are ℝ-antimagic.