TY - JOUR
T1 - Anti-magic graphs via the combinatorial NullStellenSatz
AU - Hefetz, Dan
PY - 2005/12
Y1 - 2005/12
N2 - An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges 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 has an antimagic labeling. In [10], Ringel conjectured that every simple connected graph, other than K2, is antimagic. We prove several special cases and variants of this conjecture. Our main tool is the Combinatorial NullStellenSatz (Cf. [1]).
AB - An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges 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 has an antimagic labeling. In [10], Ringel conjectured that every simple connected graph, other than K2, is antimagic. We prove several special cases and variants of this conjecture. Our main tool is the Combinatorial NullStellenSatz (Cf. [1]).
KW - Anti-magic
KW - Combinatorial NullStellenSatz
KW - Labeling
UR - http://www.scopus.com/inward/record.url?scp=30544441117&partnerID=8YFLogxK
U2 - 10.1002/jgt.20112
DO - 10.1002/jgt.20112
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AN - SCOPUS:30544441117
SN - 0364-9024
VL - 50
SP - 263
EP - 272
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 4
ER -