Efficient dominating sets in Cayley graphs. (Q1406027)
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scientific article; zbMATH DE number 1977900
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Efficient dominating sets in Cayley graphs. |
scientific article; zbMATH DE number 1977900 |
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Efficient dominating sets in Cayley graphs. (English)
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9 September 2003
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An independent set \(C\) of vertices in a graph is called an efficient dominating set if each vertex not in \(C\) is adjacent to exactly one vertex in \(C\). Efficient dominating sets are also called perfect codes. An \(E\)-chain is a countable family of nested graphs, each of which has an efficient dominating set. The authors give a constructing tool to produce \(E\)-chains of Cayley graphs. Using this tool infinite families of \(E\)-chains of Cayley graphs on symmetric groups are constructed.
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perfect code
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Hamming code
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star graph
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pancake graph
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