TY - JOUR

T1 - On antimagic directed graphs

AU - Hefetz, Dan

AU - Mütze, Torsten

AU - Schwartz, Justus

PY - 2010/7

Y1 - 2010/7

N2 - 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 (N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, Boston, 1990, pp. 108-109), Hartsfield and Ringel conjectured that every simple connected graph, other than K 2, is antimagic. Despite considerable effort in recent years, this conjecture is still open. In this article 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.

AB - 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 (N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, Boston, 1990, pp. 108-109), Hartsfield and Ringel conjectured that every simple connected graph, other than K 2, is antimagic. Despite considerable effort in recent years, this conjecture is still open. In this article 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.

KW - Antimagic

KW - Labeling

UR - http://www.scopus.com/inward/record.url?scp=77954319533&partnerID=8YFLogxK

U2 - 10.1002/jgt.20451

DO - 10.1002/jgt.20451

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AN - SCOPUS:77954319533

SN - 0364-9024

VL - 64

SP - 219

EP - 232

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 3

ER -