Antimagic Labeling of Regular Graphs

Abstract

A graph G=(V,E) is antimagic if there is a one-to-one correspondence f : E → {1, 2, . . . , |E|} such that for any two vertices u,v, ∑e∈E(u) f (e) ≠∑e∈E(v). It is known that bipartite regular graphs are antimagic and nonbipartite regular graphs of odd degree at least three are antimagic. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. In this article, we solve this problem and prove that all even degree regular graphs are antimagic.