On Zero-Sum -Magic Labelings of 3-Regular Graphs

Let G =  ( V , E ) be a finite loopless graph and let ( A , +) be an abelian group with identity 0. Then an A-magic labeling of G is a function from E into A − {0} such that for some for every , where E ( v ) is the set of edges incident to v . If exists such that a =  0, then G is zero-sum A-magic...

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Bibliographic Details
Published in:Graphs and combinatorics 2013-05, Vol.29 (3), p.387-398
Main Authors: Choi, Jeong-Ok, Georges, J. P., Mauro, David
Format: Article
Language:English
Subjects:
Combinatorics
Engineering Design
Mathematics
Mathematics and Statistics
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Summary:Let G =  ( V , E ) be a finite loopless graph and let ( A , +) be an abelian group with identity 0. Then an A-magic labeling of G is a function from E into A − {0} such that for some for every , where E ( v ) is the set of edges incident to v . If exists such that a =  0, then G is zero-sum A-magic . Let zim ( G ) denote the subset of (the positive integers) such that if and only if G is zero-sum -magic and if and only if G is zero-sum -magic. We establish that if G is 3-regular, then or
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-012-1142-6