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Anti-magic graphs via the Combinatorial NullStellenSatz

✍ Scribed by Dan Hefetz

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 111 KB
Volume: 50
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20112

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✦ Synopsis

Abstract

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 K~2~, is antimagic. We prove several special cases and variants of this conjecture. Our main tool is the Combinatorial NullStellenSatz (cf. [1]). © 2005 Wiley Periodicals, Inc. J Graph Theory

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## Abstract An __antimagic labelling__ of a graph __G__ with __m__ edges and __n__ vertices is a bijection from the set of edges of __G__ to the set of 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 tha