Total \(\alpha\)-domination in graphs (Q2839648)
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scientific article; zbMATH DE number 6187552
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total \(\alpha\)-domination in graphs |
scientific article; zbMATH DE number 6187552 |
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12 July 2013
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graph
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total \(\alpha\)-dominating set
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total \(\alpha\)-domination number
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0.98364866
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0.9348661
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Total \(\alpha\)-domination in graphs (English)
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Let \(G = (V,E)\) be a graph without isolated vertices. For some \(\alpha\) with \(0 < \alpha \leq 1\) and a set \(S \subseteq V\), we say that \(S\) is a total \(\alpha\)-dominating set if for any \(v\in V\), \(|N\cup S| \geq \alpha|N(v)|\), where \(N(v)\)is the set of all neighbors of \(v\). The cardinality of a smallest such set \(S\) is called the total \(\alpha\)-domination number of \(G\).NEWLINENEWLINENEWLINE NEWLINEIn this work some results and bounds for the total \(\alpha\)-domination number of a graph \(G\) are obtained.
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