On antimagic directed graphs

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On antimagic directed graphs
An antimagic labeling of an undirected graph G with n vertices and m edges is a bijection from the set of edges of G 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 that vertex. A graph is called antimagic if it admits an antimagic labeling. In [6], Hartsfield and Ringel conjectured that every simple connected graph, other than K2, is antimagic. Despite considerable effort in recent years, this conjecture is still open. In this paper we study a natural variation; namely, we consider antimagic labelings of directed graphs. In particular, we prove that every directed graph whose underlying undirected graph is “dense” is antimagic, and that almost every undirected d-regular graph admits an orientation which is antimagic.
Dan Hefetz, Torsten Mütze, Justus Schwartz
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JGT
Authors Dan Hefetz, Torsten Mütze, Justus Schwartz
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