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Keywords:

  • antimagic graph labeling;
  • bipartite graph;
  • regular graph;
  • graph decomposition;
  • Marriage Theorem

Abstract

A labeling of a graph G is a bijection from E(G) to the set {1, 2,… |E(G)|}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic. In this article, we show that every regular bipartite graph (with degree at least 2) is antimagic. Our technique relies heavily on the Marriage Theorem. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 173–182, 2009