On group-magic graphs (Q2747195)
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scientific article; zbMATH DE number 1657310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On group-magic graphs |
scientific article; zbMATH DE number 1657310 |
Statements
8 January 2002
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group-magic graphs
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graph labelling
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abelian group
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perfect matching
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group-magic index sets
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On group-magic graphs (English)
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Given an abelian group \(A\), a graph \(G=(V,E)\) is \(A\)-magic if there exists a labeling \(\ell\) of the edges with elements from \(A - \{0\}\) such that the induced vertex labeling \(\ell^\ast\) with \(\ell^\ast(v) = \sum \{\ell(u,v)\mid \{u,v\}\in E\}\) is a constant map. This paper gives several results on whether specific types of graphs are \(A\)-magic for abelian groups \(A\); sometimes specifically for \(A=Z_k\).
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